Input/loss method using the genetics of fossil fuels for determining fuel chemistry, calorific value and performance of a fossil-fired power plant

ABSTRACT

This invention relates to any fossil fueled thermal system, and especially relates to large commercial steam generators used in power plants, and, more particularly, to a method and apparatus for determining fuel chemistry in essentially real time based on effluents resulting from combustion, associated stoichiometrics, and the genetics of the fossil fuel. Knowing the system&#39;s fuel chemistry, the fuel calorific value, the fuel flow and the thermal performance associated with the thermal system may then be determined in essentially real time.

FIELD OF THE INVENTION

This invention relates to any fossil fueled thermal system, andespecially relates to large commercial steam generators used in powerplants, and, more particularly, to a method and apparatus fordetermining fuel chemistry in essentially real time based on effluentsresulting from combustion, associated stoichiometrics, and the geneticsof the fossil fuel. Knowing the system's fuel chemistry, the fuelcalorific value, the fuel flow and the thermal performance associatedwith the thermal system may then be determined in essentially real time.

BACKGROUND OF THE INVENTION

Although especially applicable to “The Input/Loss Method” as installedat fossil-fired power plants, this invention may also be applied to anyone of the “Input/Loss methods” installed at any thermal system burninga fossil fuel. Definitions for quoted terms are provided in the sectionentitled MEANING OF TERMS. The following paragraphs discuss prior artassociated with The Input/Loss Method and with generic Input/Lossmethods.

The principle background teachings of The Input/Loss Method aredescribed in three patents: U.S. Pat. No. 6,584,429 which issued Jun.24, 2003 and teaches a high accuracy method of determining boilerefficiency, hereinafter referred to as '429; U.S. Pat. No. 6,714,877which issued Mar. 30, 2004 and teaches how effluent concentrationsresultant from combustion may be corrected for errors, hereinafterreferred to as '877; and, most importantly, U.S. Pat. No. 6,522,994which issued Feb. 18, 2003 and teaches general methods of The Input/LossMethod. U.S. Pat. No. 6,522,994 originated as a PCT applicationresulting in the following patents: Canadian Patent 2325929; AustralianPatent 762836; and European Patent (DE, GB, GR & IT) 1171834. Thesepatents, U.S. Pat. No. 6,522,994, Canadian 2325929, Australian 762836and European 1171834, are hereinafter collectively referred to as '994.

'994 is incorporated herein by reference in its entirety. '429 isincorporated herein by reference in its entirety. '877 is incorporatedherein by reference in its entirety. In addition to '994, '429 and '877,a considerable technological foundation for The Input/Loss Method may befound in the following U.S. Pat. Nos. 6,560,563, 6,651,035, 6,691,054,6,745,152, 6,799,146, 6,810,358, 6,868,368 and 6,873,933.

Further still, related pending applications which again add to thetechnology of The Input/Loss Method include the following: CanadianPatent Application No. 2479238, European Patent Office Application No.02784559, and U.S. patent application Ser. No. 10/715,319. CanadianPatent Application No. 2479238 and European Patent Office ApplicationNo. 02784559 are the same, stemming from PCT/US02/37612 (WO2003/091881).The originating U.S. application represented by PCT/US02/37612 resultedin U.S. Pat. No. 6,651,035 which teaches how tube failures in largesteam generators may be detected using The Input/Loss Method. U.S. Pat.No. 6,651,035 was originally filed as a U.S. Continuation-In-Part to anapplication which became U.S. Pat. No. 6,745,152. U.S. patentapplication Ser. No. 10/715,319 has resulted in an allowed U.S.application which principally teaches how tube failures in RecoveryBoilers may be detected using The Input/Loss Method modified forsodium/hydrocarbon stoichiometrics, that application was published asUS2004/128111.

One of the Input/Loss methods, a rudimentary method, is described inU.S. Pat. No. 5,367,470 which issued Nov. 22, 1994 (with Dec. 14, 1989priority), and in U.S. Pat. No. 5,790,420 which issued Aug. 4, 1998.U.S. Pat. No. 5,790,420 was originally filed as a U.S.Continuation-In-Part to an application which became U.S. Pat. No.5,367,470.

Other known Input/Loss methods are thoroughly discussed in theBACKGROUND OF THE INVENTION section of '994; this discussion isreferenced herein as being important.

For many years the energy industry has attempted to categorize coals.Although there are four major ranks of coal in the U.S. classificationscheme (anthracite, bituminous, sub-bituminous and lignite), these havebeen sub-divided by ASTM D388, “Standard Classification of Coals byRank”. Refer to TABLE B1 for ASTM D388 categories (an incorrect energyconversion was used in this standard, 2.3255 kJ/kg/Btu/lb, versus 2.3260kJ/kg/Btu/lb). One problem immediately seen in TABLE B1 is its lack ofspecificity, ASTM D388 basically employs either As-Received calorificvalues, and/or proximate analyses on a dry basis to judge coals.“Ultimate Analysis” data is not employed. Higher Rank coals areclassified according to fixed carbon on a dry basis while the lower Rankcoals are classified by As-Received calorific value (wet basis). FigureX1.1 of ASTM D388 presents a typical single-variant correction betweenweight fraction of volatile matter and Reflectance in oil. A generaldiscussion of coal classifications may be found in the text TheChemistry and Technology of Coal by J. G. Speight, Marcel Dekker, Inc,New York & Base1, which discusses coal classifications in Chapter 1(pages 3-19), elemental analysis on pages 83-84 and evaluationtechniques in Chapter 8 (pages 165-199). Note that examples ofsingle-variant analyses are presented in this text's FIG. 1.2, FIG. 8.10and FIG. 8.12 and FIG. 8.11; several of these displaying weight fractionof fuel hydrogen versus weight fraction of fuel carbon. As seen, theseplots represent only broad-brush correlations, hardly capable ofsupporting of any of the Input/Loss methods. TABLE B1 ASTMClassification by Rank Rank (abbreviation) Characteristicsmeta-anthracite (ma) Fixed carbon ≧98%. anthracite (an) Fixed carbon≧92% and <98%. semi-anthracite (sa) Fixed carbon ≧86% and <92%. lowvolatile bituminous (lvb) Fixed carbon ≧78% and <86%. medium volatilebituminous (mvb) Fixed carbon ≧69% and <78%. high volatile A bituminous(hvAb) CV ≧14000 Btu/lb (CV ≧32557 kJ/kg), with Fixed carbon <69% highvolatile B bituminous (hvBb) 14000 Btu/lb > CV ≧ 13000 Btu/lb (32557kJ/kg > CV ≧ 30232 kJ/kg) high volatile C bituminous (hvCb) 13000Btu/lb > CV ≧ 10500 Btu/lb (30232 kJ/kg > CV ≧ 24418 kJ/kg)sub-bituminous A (sub A) 11500 Btu/lb > CV ≧ 10500 Btu/lb (26743 kJ/kg >CV ≧ 24418 kJ/kg) sub-bituminous B (sub B) 10500 Btu/lb > CV ≧ 9500Btu/lb (24418 kJ/kg > CV ≧ 22090 kJ/kg) sub-bituminous C (sub C) 9500Btu/lb > CV ≧ 8300 Btu/lb (22090 kJ/kg > CV ≧ 19300 kJ/kg) lignite A(lig A) 8300 Btu/lb > CV ≧ 6300 Btu/lb (19300 kJ/kg > CV ≧ 14650 kJ/kg)lignite B (lig B) 6300 Btu/lb > CV (14650 kJ/kg > CV)

There are seemingly as many coal categories used in Europe as countries.In general, Europeans categorize coal as either hard or soft dependingon ash-free calorific value. Sub-groups are then classed by volatilematter, coking properties, etc. resulting in a complex three-digitnumbering system. No European system employs Ultimate Analysis data toclassify coals, at best proximate analyses are employed. Refer to “BrownCoals and Lignites—Classification by Types on the Basis of TotalMoisture Content and Tar Yield”, International Organization forStandards, ISO 2950-1974(E).

It is also useful to recognize that the analysis of fossil fuels may beaccomplished using the Excel® computer program. Excel is owned by theMicrosoft Corporation, Redmond, Wash. state in the U.S. Excel is aregistered trademark of Microsoft Corporation. Fossil fuel data istypically obtained as Ultimate Analysis data with As-Received fuelwater, fuel ash and calorific values. As used to develop this invention,and used throughout its presentation herein, such data was analyzedusing Excel. All “R² values” mentioned herein, commonly termed theCoefficient of Determination, have been computed by Excel usingregression analysis. Excel's R² value represents the percent variationin a y-variable that is explained by the independent x-variable. Onlylinear regression was used herein. There are classical problemsassociated with R² values as are well known to one skilled instatistics. One such problem, and one important to this invention, isevident when data presents an even scatter about a linear mean. Such asituation might lead to a high R² value which does not truly reflect ay-variable being predictable by the independent x-variable (simply put,the R² value may appear acceptable, but the functionality is too coarseto be useable). The most straightforward method to address suchsituations is to simulate data patterns associated with their end useand to then evaluate the direct impact their variances have on computedoutput. For example, the impact on The Input/Loss Method's computedcalorific value of a 1.0% variance in predicted fuel carbon (and thusaffecting computed calorific value) may be assessed most conservativelyby assuming a 1.0% variance in effluent CO₂; such a 1.0% variance may beobserved, and verified, from plotted data. Another method of evaluatingdistributed data patterns is to simply apply engineering judgement bylooking at the plots: they are either unreasonable or portentfundamental understanding with obvious certainty.

The technologies underwriting The Input/Loss Method, witnessed by theaforementioned patents and patent applications, were based onrecognizing that if the effluent concentrations from combustion are usedto determine fuel chemistry, then fundamentally more unknowns areinvolved than practical equations are available. '994 presented asolution to this problem by teaching that fuel hydrogen may have afunctional relationship with fuel carbon; see Eq. (45) in '994 and thedefinition of “reference fuel characteristics” in '994. Otherrelationships are fuel oxygen versus fuel carbon, and fuel nitrogenversus fuel carbon; refer to Eqs. (43) and (44) in '994 and associateddiscussion above Eq. (42) in '994. For example, the correlationconstants A₅ & B₅ used in Eq. (45) in '994 derive directly from thedata, for example, as seen in FIG. 3 of '994. Eq. (42) in '994 presentsan explicit solution to moisture-ash-free (MAF) molar fuel carbonemploying correlation coefficients: A₃ & B₃ from MAF molar fuel oxygenas a function of MAF molar fuel carbon of Eq. (43) in '994; and A₅ & B₅from MAF molar fuel hydrogen as a function of MAF molar fuel carbon ofEq. (44) in '994. These correlations provided the missing equations.They all are simple single-variant molar correlations using hydrogenversus carbon, or oxygen versus carbon; e.g., the single-variant ismolar hydrogen as observed in '994 Eqs. (45). There was no other knownart or techniques for solving the underlying problem.

Wherein The Input/Loss Method has been installed at a number of powerplants, certain situations have arisen in which single-variantrelationships such as fuel hydrogen versus fuel carbon are simply notadequate. This has been found true when employing “reference fuelcharacteristics” as defined and taught in '994. It has been found thatthis situation is especially true if dealing with the following fueltypes: Irish peat; Powder River Basin coals; and what is termed “HighSeas” coal. Irish peat is of importance as it represents a typicalindigenous fuel source, not only for the Republic of Ireland, but alsofor Poland, for Finland and for Minnesota in the U.S. Peat's drychemistry may vary considerably given its haphazard formation asimmature coal, and its fuel water content typically varies wildly. TheMAF characteristics of peat are not unlike lignite found in Texas,Australia and Greece. Powder River Basin coals have an enormous, andgrowing, financial impact on the United States and Canada as itrepresents the largest single source of coal fuel being fired in NorthAmerican power plants. Over 120 power plants use Powder River Basincoals, growing by some estimates at 15%/year. Powder River Basin coalshave low sulfur concentrations, but are high in fuel water with highlyvariable fuel chemistries reflecting over a dozen mines located inseveral western states in the U.S. High Seas coal is defined as highenergy coal which is frequently bought, literally, while coal-carryingcargo ships are on the high seas. It may be categorized, as highvolatile bituminous coal. High Seas coal typically has low fuel water,but fuel chemistries reflecting variability associated with world-widesourcing. High Seas coal typically has calorific values in the range of25,586 to 31,401 kJ/kg (11,000 to 14,000 Btu/lbm). There are other fuelswhich, it is anticipated, will receive higher interest over the comingyears, but which will have similar variabilities. One such fuel isswitch grass, grown in the U.S. as an environmentally friendly (andrenewable) fossil fuel. Another, is wood waste (i.e., bio-mass fuel),being burned in the western states of the U.S. If Irish peat, PowderRiver Basin coals and High Seas coals were not significantly used, thenthe method taught in '994 would be adequate given a supposedwell-characterized fuel. By well-characterized is meant that neededcorrelations (e.g., MAF molar fuel hydrogen as a function of MAF molarfuel carbon) have R² values which exceed 90%. Note however that if an R²value at 90% is considered inadequate (versus, say 98%), or not, thepractical application of '994 was, indeed, limited to this level ofpredictability as a direct consequence of simple single-variantcorrelations.

It is important to note that “reference fuel characteristics”, asdefined in '994, represents a taught procedure, one in which hydrogenversus carbon relationships are developed based on historical fuel data.It does not specify usable data. When the method of '994 was installedin PRB burning powers plants, coal from specific regions within theBasin would require characterization. The Boardman Coal Plant, operatedby Portland General Electric and using The Input/Loss Method, wascharacterized specifically to PRB Decker coal. The Nebraska City Unit 1,operated by Omaha Public Power District and using The Input/Loss Method,was characterized specifically to PRB Caballo Rojo coal. And the sameeven for Irish peat. The Lough Ree Power Station, operated by theElectricity Supply Board and using The Input/Loss Method, wascharacterized specifically to Irish peat found near Lanesboro, Ireland,although the West Offlay Power Station, also burning Irish peat, not 56km (35 miles) away, was characterized specifically to the Shannonbridgeregion. '994 taught a procedure requiring historical data, requiringunique reference fuel characteristics to be programmed in a computer foreach installation. What is needed is a generic method such that a singleprocedure satisfies an entire Rank of coal, without routine need ofhistorical data. At the time of '994 there was no other known art. Whenconsidering variable fuels, as defined by poor R² values resultant fromusing simple single-variant correlations, the '994 method has not provento be generic as it suffers from a lack of flexibility under certaincircumstances.

The databases of Ultimate Analyses and calorific values used to developthis invention derive from the following sources: 1) Pennsylvania StateUniversity, Organic Petrology Laboratory database containing over 1200Ultimate Analyses and associated calorific values from over 400 mines;2) Powder River Basin coal data containing approximately 250 samplesfrom 19 different regions within the Basin; 3) so-called High Seas coaldata containing 320 samples from over 50 mines from 14 states in theU.S., South Africa, Poland, Russia and Colombia, this data includesnumerous spot analyses obtained from power plants actually using suchcoal (i.e., from the Moneypoint station, Republic of Ireland, from theBrandon Shores station, Maryland state in the U.S., and from the JorfLasfar station, Morocco); and 4) Irish peat data containingapproximately 160 samples from 6 different regions within the Republicof Ireland, notably the data having been collected over a considerabletime period, from 1963 through 2005. In total the analyzed dataconsisted of approximately 1930 Ultimate Analyses and correspondingcalorific values.

As seen in FIG. 1 for Irish peat, as seen in FIG. 3 for Powder RiverBasin coals, and as seen in FIG. 5 for High Seas coal the ability of'994 technology to reasonably provide functionality between MAF molarfuel diatomic hydrogen versus MAF molar fuel carbon is wanting, as basedon simple single-variant correlations. For the Irish peat data of FIG.1, the R² value was found at 65.90%. For the Powder River Basin coaldata of FIG. 3, the R² value was found at 71.93%. For the High Seas coaldata of FIG. 5, the R² value was found at 81.77%. Note, that althoughthese fuels are not well-characterized using single-variantcorrelations, their industrial use is quite real; such use demands animproved approach. It also must be noted that a poor R² value for MAFmolar fuel hydrogen versus MAF molar fuel carbon, portents an evenpoorer R² value for fuel oxygen versus fuel carbon; and poorer yet forfuel nitrogen versus fuel carbon. For MAF molar fuel oxygen versus MAFmolar fuel carbon, the R² values were found at 36.48% for Irish peat,14.01% for Powder River Basin coals and 64.23% for High Seas coals. Suchnon-predictability results forced the user of '994 technology, for thesetypes of fuels, to assume that MAF molar fuel oxygen be keep constant.As an example of the practical problem typical power plants using HighSeas coal (e.g., Moneypoint, Brandon Shores and Jorf Lasfar) do not sortthe fuel, they burn whatever is on the loading docks. Many power plantsuse High Seas coals sourced from around the world. An improvement ofmethods is needed if such fuels are to be described with sufficientpredictability for Input/Loss methods to function with the high accuracyof which it is capable. In summary the following features associatedwith '994 methods have proven to be inadequate:

-   -   its use of “reference fuel characteristics”, as defined in '994,        employing single-variant correlations and its use of the L₅        Factor;    -   “reference fuel characteristics”, as defined in '994, require        historical data;    -   poor R² values (<90%) for the important MAF molar fuel hydrogen        versus MAF molar fuel carbon relationships and very poor R²        values (<70%) for oxygen versus carbon relationships which        results in forcing MAF molar fuel oxygen to be held constant;    -   the use of equations which solve for elemental constituents        which combine single-variant correlation constants and        stoichiometric terms;    -   assuming fuel nitrogen is constant; and    -   the use of numerical minimum and maximum limits applied to fuel        concentrations as taught being a portion of the “reference fuel        characteristics” defined in '994, has caused inconsistencies (as        seen in FIG. 1, FIG. 3 and FIG. 5, a maximum α_(MAF-4) implies a        minimum α_(MAF-5), and typically a minimum α_(MAF-3), thus the        MAF summation could lead to inconsistencies which is an        intrinsic disadvantage of single-variant analysis).

As demonstrated in FIG. 1, FIG. 3 and FIG. 5, the method taught in '994simply cannot produce R² values near 98% for many important fuelswithout specialized study. If the fossil fuel is well characterized, andespecially if the coal is of a higher Rank and having low fuel oxygen(e.g., anthracite, semi-anthracite and sub-bituminous A) the method of'994 using single-variant correlations may produce R² values near 90%.However, if to reach predictability values at the 98% level,understanding the genesis of fossil fuels is required. It requires aclear inventive step beyond the established technology of '994. There isno known art which addresses fundamental fossil fuel genetics such thatR² values at the 98% level might be achieved, at least for the majorityof commercial fuels. Other than '994, there is no established artdirectly related to this invention. There is a clear need for amethodology which describes fossil fuel genetics in such a manner thatreliable and independent stoichiometrics may be resolved, thus allowinga “complete As-Fired fuel chemistry” determined from effluentconcentrations.

SUMMARY OF THE INVENTION

This invention relates to any fossil fueled thermal system, andespecially relates to large commercial steam generators used in powerplants, and, more particularly, to a method and apparatus fordetermining fuel chemistry in essentially real time based on effluentsresulting from combustion, associated stoichiometrics, and the geneticsof the fossil fuel based on multi-variant analysis. In addition, thisinvention teaches a device which evaluates Ultimate Analysis dataproviding diagnostic information on the sample of coal. The use of“multi-variant analysis” has lead to the discovery of the “genetics offossil fuels”, numerically defining a wide range of fossil fuels.Further extension of the multi-variant analysis technique has lead to anew L-Factor, termed L₁₀, which may be used to correct effluentconcentrations and other “Choice Operating Parameters” using '877methods. Knowing the system's fuel chemistry, the fuel calorific value,the fuel flow and the thermal performance associated with the thermalsystem may then be determined in essentially real time. The teachings ofthis invention may be implemented for monitoring any thermal systemburning a fossil fuel, or a thermal system burning a mix of fossil fuelsand inorganic fuels such as Recovery Boilers. Such monitoring is assumedto be conducted in a continuous manner (i.e., on-line, in essentiallyreal time), processing one monitoring cycle after another.

This invention, through new a method, apparatus and device, extends thetechnology associated with Input/Loss methods and teaches its industrialuse by computer producing a complete As-Fired fuel chemistry and toevaluate Ultimate Analysis data. Specifically The Input/Loss Method hasbeen applied through computer software, installable on a personalcomputer termed a “Calculational Engine”, and has been demonstrated asbeing highly useful to the operators of fossil-fired systems. TheCalculational Engine receives data from the system's data acquisitiondevice. The Calculational Engine's software consists of the ERR-CALC,EX-FOSS, FUEL and HEATRATE executable computer programs describedherein, and in '994, '429 and '877. The programs ERR-CALC and HEATRATEhaving been modified by the teachings of this invention. TheCalculational Engine continuously monitors system efficiency on-line,i.e., in essentially real time, as long as the thermal system is burningfuel. The application of this invention to The Input/Loss Methodsignificantly enhances the system operator's ability to understandcoal-fired power plants.

The present invention provides a procedure, termed multi-variantanalysis, which allows discovery of the genetics of fossil fuels, fromwhich generates matrix solution to fuel chemistry based on effluents(“Choice Operating Parameters”).

The present invention provides a new L-Factor, termed L₁₀, which allowseffluents from combustion to be corrected using the methods taught in'877. The high consistency observed in L₁₀ has resulted directly fromthe genetics of the fossil fuel as based on multi-variant analysis.

The present invention, founded on multi-variant analysis, also teacheshow fuel flow may be computed, and with a determined boiler efficiencyand knowing the energy flow to the working fluid, results in a systemthermal efficiency through which the system operator receivesessentially real time feed-back as to whether his/her adjustments to thesystem do good or harm to efficiency.

The present invention teaches a new method to classify coals, replacingor improving common standards such as ASTM D388 and ISO 2950. Thepresent invention also provides a method and device to distinguish dataoutliers associated with Ultimate Analyses.

Other objects and advantages of the present invention will becomeapparent when its general methods are considered in conjunction with theaccompanying drawings and the related inventions of '994, '429 and '877.

According to a first embodiment the present invention provides a methodfor quantifying the operation of a thermal system burning a fossil fuelhaving a heat exchanger/combustion region producing combustion products,the method comprising the steps of:

before on-line operation,

-   -   using a genetics of the fossil fuel based on multi-variant        analysis; and

while operating on-line,

-   -   using a mathematical description of the thermal system,

the step of operating on-line comprising the steps of

-   -   measuring a set of measurable Operating Parameters, including at        least effluent concentrations of O₂ and CO₂, these measurements        being made at a location downstream of the heat        exchanger/combustion region of the thermal system,    -   obtaining an effluent concentration of H₂O, as an obtained        effluent H₂O,    -   obtaining a fuel ash concentration selected from the group        consisting of: a constant value of fuel ash, a predictable value        of fuel ash, a measured value of fuel ash determined from a fuel        ash instrument and a value of fuel ash determined from explicit        solution, as an obtained fuel ash concentration,    -   obtaining a concentration of O₂ in the combustion air local to        the system,    -   obtaining an Air Pre-Heater Leakage Factor, and    -   operating a programmed computer to obtain a complete As-Fired        fuel chemistry, including fuel water and fuel ash, based on the        genetics of the fossil fuel, the mathematical description, the        set of measurable Operating Parameters, the obtained effluent        H₂O, the obtained fuel ash concentration, the concentration of        O₂ in the combustion air local to the system and the Air        Pre-Heater Leakage Factor.

According to a second embodiment the present invention provides a methodfor quantifying the operation of a thermal system burning a fossil fuelhaving a heat exchanger/combustion region producing combustion products,the method comprising the steps of:

before on-line operation,

-   -   developing a genetics of the fossil fuel based on multi-variant        analysis; and

while operating on-line,

-   -   developing a mathematical description of the thermal system,

the step of operating on-line comprising the steps of

-   -   measuring a set of measurable Operating Parameters, including at        least effluent concentrations of O₂ and CO₂, these measurements        being made at a location downstream of the heat        exchanger/combustion region of the thermal system,    -   obtaining an effluent concentration of H₂O, as an obtained        effluent H₂O,    -   obtaining a fuel ash concentration selected from the group        consisting of: a constant value of fuel ash, a predictable value        of fuel ash, a measured value of fuel ash determined from a fuel        ash instrument and a value of fuel ash determined from explicit        solution, as an obtained fuel ash concentration,    -   obtaining a concentration of O₂ in the combustion air local to        the system,    -   obtaining an Air Pre-Heater Leakage Factor, and    -   operating a programmed computer to obtain a complete As-Fired        fuel chemistry, including fuel water and fuel ash, based on the        genetics of the fossil fuel, the mathematical description, the        set of measurable Operating Parameters, the obtained effluent        H₂O, the obtained fuel ash concentration, the concentration of        O₂ in the combustion air local to the system and the Air        Pre-Heater Leakage Factor.

One of the advantages of these method embodiments is that they allow thegenetics of fossil fuels to be determined based on multi-variantanalysis. As will be apparent from the following description, eachfossil fuel has unique molecular characteristics which are now knowable.Thus, as has been found when developing this invention, multi-variantrelationships differ between broad fuel types, and differ consistently.A further advantage of the methodologies of the present invention isthat they allow elucidation of the genetics of fossil fuels such that areliable set of independent equations, including stoichiometricequations independent of correlation constants, can be formed to resolvea complete As-Fired fuel chemistry based on effluent concentrations bymatrix solution.

According to a third embodiment the present invention provides for anapparatus for assisting the operation of a thermal system burning fossilfuel, the apparatus comprising:

a data acquisition device to collect data from the thermal systemincluding at least a selection of Choice Operating Parameters, the dataacquisition device producing a set of acquired system data;

a computer with a processing means;

a set of instructions for configuring the processing means to determinea fuel chemistry of the fossil fuel and to receive as input the set ofacquired system data, resulting in a programmed computer;

means by which the programmed computer receives as input the set ofacquired system data;

the programmed computer producing the fuel chemistry of the fossil fuel;and

means for reporting the fuel chemistry of the fossil fuel to assist inthe operation of the thermal system.

According to a forth embodiment the present invention provides a devicefor evaluating an Ultimate Analysis of a coal sample, the devicecomprising:

a set of instruments capable of producing the Ultimate Analysis of acoal sample and to produce an Ultimate Analysis output, said outputcomprising at least carbon, hydrogen and oxygen concentrations;

a data processing device with a processing means and a memory meanswherein the memory means stores a set of descriptive fossil fuel databased on the genetics of fossil fuels organized by categories;

a set of instructions for configuring the processing means to comparethe Ultimate Analysis with the set of descriptive fossil fuel data andto receive as input the Ultimate Analysis output from the set ofinstruments, resulting in a programmed data processing device capable ofproducing a comparative report on the Ultimate Analysis;

the set of instruments producing the Ultimate Analysis output;

means of communicating the Ultimate Analysis output from the set ofinstruments to the programmed data processing device;

the data processing device producing the comparative report on theUltimate Analysis; and

means of communicating the comparative report on the Ultimate Analysis.

One of the advantages of the apparatus embodiment of this invention isthat it provides a computing vehicle for calculating a real timecomplete As-Fired fuel chemistry of a coal-fired power plant, providingneeded information to the operator. Also, one of the advantages of thedevice embodiment of this invention is that it provides a computingvehicle for evaluating Ultimate Analysis data, providing diagnosticinformation on coal sample analyses. Both of these advantages stem fromthe consistency found in the genetics of fossil fuels.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 (prior art) is a plot of MAF molar fuel diatomic hydrogen versusMAF molar fuel carbon for Irish peat following the teachings of '994,and as such it is considered prior art. The resultant R² value is65.90%.

FIG. 2 is a plot of MAF molar fuel diatomic hydrogen plus MAF molar fueldiatomic oxygen versus MAF molar fuel carbon for Irish peat followingthe teachings herein, using the same Ultimate Analysis data as was usedfor FIG. 1. The resultant R² value is 98.45%. Refer to TABLE 4 forfunctionalities.

FIG. 3 (prior art) is a plot of MAF molar fuel diatomic hydrogen versusMAF molar fuel carbon for Powder River Basin coals following theteachings of '994, and as such it is considered prior art. The resultantR² value is 71.93%.

FIG. 4 is a plot of MAF molar fuel diatomic hydrogen plus MAF molar fueldiatomic oxygen versus MAF molar fuel carbon for Powder River Basincoals following the teachings herein, using the same Ultimate Analysisdata as was used for FIG. 3. The resultant R² value is 99.77%. Refer toTABLE 4 for functionalities.

FIG. 5 (prior art) is a plot of MAF molar fuel diatomic hydrogen versusMAF molar fuel carbon for high volatile bituminous coals following theteachings of '994, and as such it is considered prior art. This plotencompasses the following Ranks: high volatile A bituminous (hvAb), highvolatile B bituminous (hvBb), high volatile C bituminous (hvCb), andsamples of High Seas commercial coal. The resultant R² value is 81.77%.

FIG. 6 is a plot of MAF molar fuel diatomic hydrogen plus MAF molar fueldiatomic oxygen versus MAF molar fuel carbon for high volatilebituminous coals following the teachings herein, using the same UltimateAnalysis data as was used for FIG. 5. The resultant R² value is 99.77%.Refer to TABLE 4 for functionalities.

FIG. 7A is a repeat of FIG. 5, using its data, but also indicating botha +3.116% and a −3.116% variance of MAF molar fuel diatomic hydrogen fora given MAF molar fuel carbon. Observe that the preponderance of thedata, although evenly distributed, is encompassed within a ±3.116%variance.

FIG. 7B is a demonstration, using the Excel spreadsheet program, of whata ±3.116% variance means to the computation of R². The samefunctionality of data was used as associated with FIG. 5 and FIG. 7A.The same average frequency in data variation was also applied, resultingin the same R² as found for FIG. 5, at 81.77%. Also plotted in FIG. 7Bis a ±0.840% variance, resulting in an R² of 98.45% (see TABLE 4 andTABLE 5 for detailed results).

FIG. 8 is a plot of MAF molar fuel carbon plus MAF molar fuel diatomichydrogen versus MAF molar fuel diatomic oxygen. This plot encompassesthe following Ranks of coal: anthracite (an), sem-anthracite (sa) andsub-bituminous B (sub B). FIG. 8 follows the teachings of thisdisclosure. Refer to TABLE 2 for functionalities.

FIG. 9 is a plot of MAF molar fuel carbon plus MAF molar fuel diatomicoxygen versus MAF molar fuel diatomic hydrogen. This plot used the sameUltimate Analysis data as was used for FIG. 8 and follows the teachingsof this disclosure. Refer to TABLE 3 for functionalities.

FIG. 10 is a plot of MAF molar fuel diatomic hydrogen plus MAF molarfuel diatomic oxygen versus MAF molar fuel carbon. This plot used thesame Ultimate Analysis data as was used for FIG. 8 and follows theteachings of this disclosure. Refer to TABLE 4 for functionalities.

FIG. 11 is a plot of MAF molar fuel carbon plus MAF molar fuel diatomichydrogen versus MAF molar fuel diatomic oxygen. This plot encompassesthe following fossil fuels: lignite A (lig A), samples of Greek lignite(lig B) and Irish peat. Refer to TABLE 2 for functionalities.

FIG. 12 is a plot of MAF molar fuel carbon plus MAF molar fuel diatomicoxygen versus MAF molar fuel diatomic hydrogen. This plot used the sameUltimate Analysis data as was used for FIG. 11. Refer to TABLE 3 forfunctionalities.

FIG. 13 is a plot of MAF molar fuel diatomic hydrogen plus MAF molarfuel diatomic oxygen versus MAF molar fuel carbon. This plot used thesame Ultimate Analysis data as was used for FIG. 11. Refer to TABLE 4for functionalities.

FIG. 14 is a plot of MAF molar fuel carbon plus MAF molar fuel diatomicoxygen versus MAF molar fuel diatomic hydrogen. This plot encompassesthe following Ranks of coal: anthracite (an), semi-anthracite (sa),sub-bituminous A (sub A), sub-bituminous B (sub B), sub-bituminous C(sub C) and lignite A (lig A). FIG. 14 follows the teachings of thisdisclosure. FIG. 14 represents the bases for generic determination ofeffluent CO₂ for a wide variety of fossil fuels. Refer to TABLE 3 forfunctionality.

FIG. 15 is a plot of the L₁₀ Factor versus MAF molar fuel diatomicoxygen for high volatile bituminous and High Seas coals using FIG. 5(FIG. 6 and FIG. 7A) data, with the exception of hvCb. FIG. 15 followsthe teachings of this disclosure. The Ultimate Analysis data of HighSeas coal were found more similar to hvAb and hvBb than hvCb, thus hvCbwas dropped such that the resultant average MAF chemistry would liewithin the High Seas database (an arbitrary choice). The resultant R²value is 97.27%. Refer to TABLE 7 for functionalities.

FIG. 16 is a plot of the L₁₀ Factor versus MAF molar fuel carbon plusMAF molar fuel diatomic hydrogen for high volatile bituminous and HighSeas coals using the same Ultimate Analysis data as was used for FIG. 5(FIG. 6, FIG. 7A and FIG. 15). FIG. 16 follows the teachings of thisdisclosure. The resultant R² value is 99.25%. Note that a corrected L₁₀is also plotted indicating an essentially constant L₁₀, following theteaching of Eq. (73). Refer to TABLE 8 for functionalities.

FIG. 17 is a plot of the L₁₀ Factor versus MAF molar fuel diatomicoxygen. This plot used the same Ultimate Analysis data as was used forFIG. 11. Refer to TABLE 7 for functionalities.

FIG. 18 is a plot of the L₁₀ Factor versus MAF molar fuel carbon plusMAF molar fuel diatomic hydrogen. This plot used the same fuels as forFIG. 11. Refer to TABLE 8 for functionalities.

FIG. 19 is a schematic representation of a steam generator illustratingthe application of stoichiometric relationships, and also containsdefinitions of some of the important terms used herein.

FIG. 20A, FIG. 20B and FIG. 20C is a block diagram of the generalinteractions and functions of The Input/Loss Method and supportingcomputer programs ERR-CALC, FUEL, EX-FOSS and HEATRATE used to implementthis invention; herein collectively referred to as FIG. 20. FIG. 20 alsoillustrates “Fuel Iterations” involving FUEL, EX-FOSS and HEATRATE.

FIG. 21 is a plot of an emulation of a power plant, using the methodstaught herein, in which the system's measured relative humidity is beingessentially matched by a computed relative humidity demonstratingstoichiometric understanding. The indicated plant fuel flow wasdemonstrated to have a bias of 2.4%.

FIG. 22 is a representation of the apparatus of this invention showing acomputer receiving Operating Parameters data including a selection ofChoice Operating Parameters, from a power plant and producing outputreports of computed quantities as taught herein.

DESCRIPTION OF THE PREFERRED EMBODIMENT

To assure an appropriate teaching of this invention, its description isdivided by sub-sections. The first two present nomenclature, definitionsof equation terms, typical units of measure, and meaning of terms usedherein (such as Choice Operating Parameters and System EffectParameters, the genetics of the fossil fuel, etc.). The remainingsub-sections, representing the bulk of the teachings, are divided asfollows: system stoichiometrics; genetics of fossil fuels; the L₁₀Factor and its use; determining complete As-Fired fuel chemistry;determining calorific value, boiler efficiency, fuel and effluent flows;correcting Choice Operating Parameters which includes a discussion onbenchmarking real time monitoring systems; and the Calculational Engineapparatus required to operate this invention. These principle sectionsare then followed by a conclusion, THE DRAWINGS and related teachings.Determining a high accuracy boiler efficiency is taught in '429.Teachings of multidimensional minimization techniques, as applicable tothis invention are presented in '877. The present invention expands theaccuracy and consistency of all Input/Loss methods when monitoringfossil fired steam generators in real time, and specifically builds uponand expands the utility of The Input/Loss Method described herein and in'994, '429 and '877.

Definitions of Equation Terms and Typical Units of Measure

Stoichiometric Terms:

-   a=Moles of combustion O₂ input to the system; moles/base.-   aβ=O₂ entering with system air leakage (typically via the air    pre-heater); moles/base.-   a_(DRY-theor)=Moles of combustion O₂ input to the system required    for theoretical combustion associated with Dry (water free) fuel;    moles/base.-   A_(Act)=Concentration of O₂ in combustion air local to (and    entering) the system as combustion air; the reference value for    A_(Act) is taken as 0.20948 obtained from the United States National    Aeronautics and Space Administration (U.S. Standard Atmosphere 1976,    NOAA-S/T-76-1562-NASA); molar fraction.-   b_(A)=Moisture in the entering combustion air; directly proportional    to the ambient air's specific humidity (ω_(Act)); moles/base.-   =ω_(Act)a(1.0+φ_(Act))N_(DRY-AIR)/N_(H2O)-   b_(A)β=Moisture entering with system air leakage; moles/base.-   b_(Z)=Moles of known water in-leakage entering and mixing with the    combustion gases; moles/base.-   b_(PLS)=Moles of pure limestone (CaCO₃) required for zero effluent    CaO production moles/base.-   ≡k_(F)−k_(Act)−r-   d_(Act)=Total effluent CO₂ at the system's boundary (i.e., Stack);    moles/base.-   g=Calculated effluent O₂ at the system's boundary without air    leakage; moles/base.-   G_(Act)=Total effluent oxygen at the system's boundary (g+aβ);    moles/base.-   G_(OHC1)=Fitting intercept constant for L₁₀ versus MAF molar fuel    diatomic oxygen; molar fraction.-   G_(OHC2)=Fitting intercept constant for L₁₀ versus MAF molar fuel    carbon plus MAF fuel hydrogen; molar fraction.-   H_(OHC1)=Fitting slope constant for L₁₀ versus MAF molar fuel    diatomic oxygen; molar fraction.-   H_(OHC2)=Fitting slope constant for L₁₀ versus MAF molar fuel carbon    plus MAF molar fuel diatomic hydrogen; molar fraction.-   j=Calculated effluent H₂O at the system's boundary without air    leakage; moles/base.

J_(Act)=Total effluent water at the system's boundary (j+ b_(A)β);moles/base.

-   J_(theor)=Total effluent water at the system's boundary based on    theoretical combustion of dried fuel; moles/base.-   J_(OHCk)=Fitting intercept constant for MAF molar fuel quantities    (k=1 for C+H, k=2 for C+O, and k=3 for H+O); molar fraction.-   k_(Act)=Effluent SO₂ measured at the system's boundary; moles/base.-   k_(F)=A computed SO₂ equivalent to fuel sulfur (xα₆) but less SO₃    production, and before limestone conversion or ash capture;    moles/base.-   ≡xα₆ (1.0−Γ_(SO3)).-   K_(OHCk)=Fitting slope constant for MAF molar fuel quantities (k=1    for C+H, k=2 for C+O, and k=3 for H+O); molar fraction.-   l=Effluent SO₃ at the system's boundary, a computed quantity;    moles/base.-   n_(i)=Molar quantities of dry gaseous effluents of combustion at the    system boundary, without the air leakage term; specifically those    products associated with the following quantities:    -   d_(Act), g, h, k_(Act), e_(Act), f, l, m, p, q, t and u;    -   note: Σn_(i≡)100 moles of dry gaseous effluent at the Stack is        the assumed calculational “base” for Eq. (29F), see FIG. 19;        moles/base.-   n_(ii)=Molar quantities of non-gas products of combustion at the    system boundary, without the moisture term associated with air    leakage, specifically those products associated with the following    quantities:    -   j, r, xα₁₀, (1.0+γ)b_(PLS), v and w; see Eq. (29F) and FIG. 19;        moles/base.-   N_(k)=Molecular weight of compound k.-   r=SO₂ captured by effluent ash; moles/base.-   R_(Act)=Ratio of moles of dry non-atmospheric gas from the    combustion process before entering the air pre-heater to the diluted    non-atmospheric gas leaving, typically: (Moles of CO₂ entering the    air pre-heater)/(Moles of CO₂ leaving the air pre-heater); defined    as the Air Pre-Heater Leakage Factor; note that R_(Act) may be    assumed to be unity (=1.00) indicating no leakage is present (as may    be assumed with Tubular Air Heaters); molar fraction.-   R′_(Act)=Ratio of moles of dry atmospheric gas from the combustion    process before entering the air pre-heater to the enriched    atmospheric gas leaving, typically: (Moles of O₂ entering the air    pre-heater)/(Moles of O₂ leaving the air pre-heater); molar    fraction.-   x=Moles of As-fired fuel required per 100 moles of dry gaseous    effluent; moles/base.-   x_(theor)=Moles of As-Fired fuel associated with theoretical    combustion of dried fuel; moles/base.-   x_(DRY-theor)=Moles of Dry fuel associated with theoretical    combustion of dried fuel; moles/base.-   x_(MAF-theor)=Moles of Moisture-Ash-Free (MAF) fuel associated with    theoretical combustion of dried fuel; moles/base.-   xα₁₀=Mineral matter in As-Fired fuel, the terms “mineral matter” and    “ash” are used interchangeably; moles/base.-   z=Moles of H₂O per mole of CaSO₄, supplied as input based on    periodic laboratory analysis of boiler refuse, a minor term; molar    fraction.-   α_(k)=As-Fired (wet-base) fuel constituent k per mole of fuel;    -   Σα_(k)=1.0, where: k=1, 2, 3, 4, 5, 6, 10; see Eq. (29F)    -   therein for terms; mole-k/mole-fuel.-   α_(MAF-k)=Moisture-Ash-Free (MAF) fuel constituent k per mole of MAF    fuel;    -   Σα_(MAF-k)=1.0, where: k=1, 3, 4, 5, 6; see Eq. (29F) therein        for terms; mole-k/mole-fuel.-   β=Air Pre-Heater Dilution Factor (ratio of air leakage to true    combustion air); note that β=f(R′_(Act)) is defined by Eqs. (23) and    (24); molar fraction-   β≡100(R_(Act)−1.0)/[a R_(Act)(1.0+φ_(Act))]-   σ=Kronecker function: unity if α₆>0.0, zero if no sulfur is present    in the fuel.    γ=Molar ratio of excess CaCO₃ to stoichiometric CaCO₃ (e.g., γ=0.0    if no effluent CaO is present); molar fraction.-   γ=[(m_(LS)/m_(AF))×N_(AF)/(ξb_(PLS)N_(CaCO3))]−1.0; where m_(LS) is    the system's indicated plant limestone flow, and ξ is a mass ratio    of actual limestone to pure CaCO₃ it contains.-   Γ_(SO3)=Ratio of effluent SO₃ (l) to total fuel sulfur, xα₆; see Eq.    (29F); molar ratio-   ≡l/(k_(F)+l)-   Γ_(ESP)=Ratio of SO₂ at the system boundary, to SO₂ found before ash    capture (i.e., before the Electrostatic Precipitator or    desulfurization system) and after limestone conversion; molar ratio-   ≡k_(Act)/(k_(Act)+r)-   φ_(Act)=Ratio of non-oxygen gases (N₂ and Ar) to oxygen in the    combustion air; molar ratio.-   φ_(Act)≡(1.0−A_(Act))/A_(Act)-   φ_(Ref)=Reference ratio of non-oxygen gases (principally N₂ and Ar)    to oxygen in the combustion air taken as 3.7737254 as being based on    A_(Act)=0.20948; molar ratio.

Quantities Related to System Terms:

-   AF_(input)=Indicated Air/Fuel ratio defined by the indicated air    flow and m_(AF-PLT); unitless mass ratio.-   AF_(Act)=Normalized Air/Fuel ratio; unitless mass ratio.-   BBTC=Energy flow to the working fluid heated by combustion products;    kJ/hr (Btu/hr).

H_(Act)=Relative humidity of ambient air local to the thermal system asa function of the psychrometric state; see Operating Parameters;fraction.

-   HBC≡Firing Correction; kJ/kg_(AF)(Btu/lbm_(AF)).-   HHV_(AF)=Gross (or higher) calorific value;    kJ/kg_(AF)(Btu/lbm_(AF)).-   HHVP=As-Fired gross calorific value, based on HHV_(AF) and used in    system evaluations as corrected for a constant pressure process;    kJ/kg_(AF) (Btu/lbm_(AF)).-   HR=System heat rate (HHV-based as HR_(HHV); or LHV-based as    HR_(LHV)); kJ/kWh (Btu/kWh).-   LHV_(AF)=Net calorific value based on the measured or calculated    gross calorific value (HHV_(AF)); kJ/kg_(AF)(Btu/lbm_(AF)).-   LHVP=As-Fired net calorific value, based on LHV_(AF) and used in    system evaluations as corrected for a constant pressure process;    kJ/kg_(AF) (Btu/lbm_(AF)).-   m_(AF)=As-Fired fuel flow; kg_(AF)/hr (lbm_(AF)/hr).-   m_(AF-pLT)=Indicated plant fuel flow; kg_(AF)/hr (lbm_(AF)/hr).-   m_(LS)=Indicated plant limestone flow associated with a thermal    system such as a fluidized bed thermal system; kg_(AF)/hr    (lbm_(AF)/hr).-   m_(T)=Tube leakage flow; kg_(AF)/hr (lbm_(AF)/hr).-   T=Temperature; ° C. (° F.).-   T_(Amb)≡Ambient temperature local to the system, ° C. (° F.).-   T_(Cal)≡Calorimetric temperature to which calorific value is    referenced; ° C. (° F.).-   T_(Stack)≡Boundary temperature of the system effluents, the effluent    temperature, defines the “Stack”; ° C. (° F.).-   W_(output)=Gross power generated from a power plant; kWe.-   η_(SYS)=System efficiency (HHV-based as η_(SYS-HHV); or LHV-based as    η_(SYS-LHV)); unitless-   η_(B)=Boiler efficiency (HHV-based as η_(B-HHV); or LHV-based as    η_(B-LHV)); unitless.-   ω_(Act)=Specific humidity of ambient air local to the thermal system    as a function the psychrometric state; see Operating parameters;    kg-moisture/kg-dry-air (lbm-moisture/lbm-dry-air).

Subscripts and Abbreviations:

-   Act=Actual value obtained from the operating thermal system.-   AF=As-Fired condition at the thermodynamic boundary (e.g., if fuel,    As-Fired is wet with water and mineral matter).-   DRY=Dry chemical base (i.e., free of water).-   MAF=Moisture-Ash-Free chemical base (i.e., free of water and free of    mineral matter).-   PLS=Pure limestone (CaCO₃).-   Ref=Reference value.-   theor=Refers to conditions associated with theoretical combustion of    dried fuel.    Meaning of Terms

The words “Operating Parameters”, as taken within the general scope andspirit of the present invention, mean common data obtained from athermal system applicable to the thermodynamic understanding of thatsystem. The following quantities may be included in the definition ofOperating Parameters, they are not encompassing but considered typicalof a minimum set of data required for such thermodynamic understanding:effluents CO₂ and O₂ concentrations determined at the Stack, or beforethe air pre-heater (Boiler side of the air pre-heater); effluent SO₂concentration if fuel sulfur is present, determined at the Stack, orbefore the air pre-heater (Boiler side of the air pre-heater); the mass,wet-base ratio of the indicated combustion air flow at the system'scombustors, to the indicated plant fuel flow, termed AF_(Act) (note thatAF_(Act) is obtained only for the determination of fuel ash as taughtherein); effluent H₂O concentration measurement, or assumptions made (oras otherwise may be determined); effluent temperature measurement, thatis the average temperature associated with the combustion gases at thesystem boundary (caution must be exercised in measuring non-stratifiedgas flows); the inlet/outlet ratio of CO₂ (producing R_(Act) as ispreferred), or O₂ (producing R′_(Act)) across the air pre-heater wherethese ratios could be obtained on-line, off-line, based on periodictesting or judgement of such ratios used for the determination of airpre-heater leakage; determination of fuel temperature at an appropriatesystem boundary; air psychrometric measurements leading to relative andspecific humidities, or as otherwise determined, at the system boundary(e.g., dry and wet bulb temperatures, or dry bulb and relative humidity,or dry bulb and dew point temperatures); quantities comprising thesystem's Firing Correction term, HBC as taught in '429; the dischargetemperatures of the air as it exits each air heating or cooling devicebut before it reacts with the fuel (for example, such devices mightinclude the air pre-heater, forced-draft fan, steam-to-air heater,etc.); and similar quantities. Operating Parameters also include a basicunderstanding of the fuel being burned: its general classification, itsgeneral water and its ash contents, and typical calorific values to beexpected. Operating Parameters include the energy flow to the workingfluid heated by combustion products (BBTC). For a typical steamgenerator, the measurements required to determine BBTC typically includefeedwater flow to the steam generator, feedwater pressure andtemperature, determination of the steam flow from the steam generator ifdifferent than the feedwater flow, steam pressure, steam temperature orquality (or assumed quality), and, if applicable, reheat flows, andreheat inlet and outlet pressures and temperatures. If employing aReheater heat exchanger, determination of accurate reheat flowsgenerally requires understanding of steam turbine flow distributions(involving high pressure turbine shaft seals, steam flows to feedwaterheaters, turbine bypass leakages, attemperation spray flows and thelike). Operating Parameters also include the electrical generationproduced (W_(output)) if the working fluid powers a turbine-generatorcycle.

The words “Choice Operating Parameters” (COP), as taken within thegeneral scope and spirit of the present invention, are defined asmeaning any sub-set of Operating Parameters which directly impact systemstoichiometrics, and thus may impact the determination of fuel chemistryas taught herein. This invention assumes that Choice OperatingParameters may have error, said error may adversely affect thedetermination of fuel chemistry, but said error may be corrected astaught herein and through the optimization methods of '877. In thePreferred Embodiment Choice Operating Parameters are selected by theuser of this invention from an available set. This available set ofChoice Operating Parameters includes the following nine: 1) effluent CO₂concentration measured at the Stack or Boiler; 2) H₂O concentrationmeasured, or as otherwise may be determined, at the Stack or Boiler; 3)the mass, wet-base ratio of the indicated combustion air flow at thesystem's combustors, to the indicated plant fuel flow, the Air/Fuelratio termed AF_(Act); 4) the Air Pre-Heater Leakage Factor, termedR_(Act), which may be ≧1.00, where unity (=1.00) indicates no leakage ispresent (as may be the case with Tubular Air Heaters); 5) theconcentration of O₂ in the combustion air local to the system, or asotherwise determined, termed A_(Act) (leading to the determination ofφ_(Act)); 6) the system's indicated plant limestone flow, termed m_(LS);7) effluent O₂ concentration measured at the Stack or Boiler; 8) massflow associated with a heat exchanger tube leakage, termed m_(T); and 9)the relative humidity of the ambient air local to the thermal system andwhich is associated with its combustion air, termed H_(Act).

The words “System Effect Parameters” (SEP), as taken within the generalscope and spirit of the present invention, mean any parameter of thethermal system or its fuel which directly impacts the determination ofsystem efficiency. In the most general sense System Effect Parametersinclude any parameter used in Eqs. (103), (104A) through (107B) whichcompute system efficiency and thus system heat rate. For the PreferredEmbodiment, System Effect Parameters include the following four types ofquantities: the L₁₀ Factor; the computed As-Fired fuel flow (m_(AF));the gross calorific value (either HHV_(AF), HHV_(DRY) or HHV_(MAF)); andthe As-Fired fuel water fraction (WF_(H2O)) which may be used fordetermination of tube leakage or to convert HHV_(DRY) to HHV_(AF). Thecomputed L₁₀ Factor affects fuel chemistry which affects calorific valueand boiler efficiency, and thus has an immediate impact on systemefficiency. “Reference System Effect Parameters” are constant andtargeted (i.e., desired) System Effect Parameters to which the SystemEffect Parameters are numerically driven by the minimization techniquesthrough optimizing a selection of Choice Operating Parameters.

The words “Input/Loss methods”, as taken within the general scope andspirit of the present invention, mean any method or combination ofmethods in which one or more of the following parameters is determinedbased on effluent concentrations and/or a selection of Choice OperatingParameters: moisture-ash-free fuel chemistry, dry fuel chemistry (i.e.,water free), complete As-Fired fuel chemistry, fuel calorific value(i.e., fuel heating value), boiler efficiency, fuel flow, and/oreffluent flow. In addition to '994, '429 and '879 and related patents,Input/Loss methods include the methods of U.S. Pat. Nos. 5,367,470 and5,790,420. The words “The Input/Loss Method” refers specifically to thecollection of technologies described in '994, '429 and '879, in additionto the teachings disclosed herein.

As used herein, the words “Calculational Engine” refers to a computerwith a processing means and a memory means. Typically said computer is acommon personal computer in which software descriptive of The Input/LossMethod as taught herein is installed (i.e., resulting in a programmedcomputer). Said computer may also include, broadly, any data processingunit such as a specialized computer, a hand-held computer, or anintegrated circuit, all of which are capable of receiving sets ofinstructions and has memory (i.e., having a processing means and amemory means).

As used herein, if used, the words “obtain”, “obtained”, “obtaining”,“determine”, “determined”, “determining”, “determination”, “establish”,“established” or “establishihg” are defined as measuring, calculating,computing, assuming, estimating or gathering from a database.

As used herein, the words “monitoring” or “monitored” are meant toencompass both on-line monitoring (i.e., processing system data inessentially real time) and off-line monitoring (i.e., computationsinvolving static data). A “monitoring cycle” is meant to be oneexecution of the processes described in FIG. 20B and FIG. 20C.

As used herein, the words “smoke Stack” or “Stack” or “system boundary”are defined as the physical boundary of the thermal system where gaseouscombustion effluents exit, entering the local environment; refer to 43in FIG. 19, further discussed within THE DRAWINGS. Solid effluents suchas ash, not leaving the Stack, are referenced to the generic system'sboundary 44 in FIG. 19.

As used herein, the words “Boiler” or “Boiler Effluent” are defined asthe region 35 in FIG. 19, or generically between the physical exit ofthe system's region 34 in FIG. 19 and entrance to its air pre-heater 36in FIG. 19; see THE DRAWINGS.

As used herein, the words “Fuel Iterations” are defined in conjunctionwith a detailed description of FIG. 20 found within THE DRAWINGS.

As used herein, the word “indicated” when used in the context of dataoriginating from the thermal system is defined as the system's actualand uncorrected measurements of a physical process (e.g., pressure,temperature, mass flow, volumetric flow, density, and the like) whoseaccuracy or inaccuracy is not assumed. As examples, a system's“indicated plant fuel flow” or its “indicated plant limestone flow”denote system measurements the accuracy of which is unknown (they are“as-is”, with no judgement applied). Such indicated measurements aresaid to be either correctable or not. If not correctable, it may be thatthe associated computed value from Input/Loss methods tracks theindicated value over time (the indicated not being corrected per se). Inthe case of indicated plant limestone flow when used as a ChoiceOperating Parameter (Λ₆), it is directly corrected as taught by thisinvention. In the case of indicated plant fuel flow when used as aSystem Effect Parameter, it may be shown that the computed fuel flow,m_(AF), tracks the indicated plant fuel flow, m_(AF-pLT).

As used herein, the words “genetics of fossil fuels” or “genetics of thefossil fuel” are defined as the specific chemical patterns found commonto certain fossil fuels as based on “multi-variant analysis”. Geneticsof fossil fuels results in elemental patterns numerically descriptive ofmolar relationships, for example the CH_(c2)O_(c3) relationships astaught through TABLE 6. As defined, the term derives from the word“genesis” taken, in the context of this invention, as meaning tounderstand the chemical formation of fossil fuels. Multi-variantanalysis consists of a combination of two or more elemental fuelconstituents, multiplied by the same quantity, related mathematically toanother elemental fuel constituent. The combination of two or moreelemental fuel constituents may be dependent or independent quantities.Multi-variant analysis used herein comprise the following: combined MAFmolar fuel carbon plus MAF molar fuel hydrogen as a function of MAFmolar fuel oxygen; combined MAF molar fuel carbon plus MAF molar fueloxygen as a function of MAF molar fuel hydrogen; or combined MAF molarfuel hydrogen plus MAF molar fuel oxygen as a function of MAF molar fuelcarbon. Examples are found in Eqs. (61), (62), (63) and (72), and whenEq. (71) is combined with Eq. (72) eliminating L₁₀. Note that theserelationships and Eqs. (61), (62) and (63) employ diatomic hydrogen anddiatomic oxygen, consistent with Eq. (29F), which is the PreferredEmbodiment. Although the early discovery work anticipated specifying amolecular pattern using monatomic hydrogen and monatomic oxygen, boththe monatomic and diatomic analyses produced essentially the same highCoefficients of Determination (if consistency developed). The diatomicis the Preferred Embodiment only since it is consistent with thecombustion equation, Eq. (29F), thus eliminating conversion betweendifferent MAF bases. Also, there are other multi-variant analysis typeswhich may be considered such as: combined MAF molar fuel carbon plus MAFmolar fuel hydrogen plus MAF molar fuel sulfur as a function of MAFmolar fuel oxygen; MAF molar fuel carbon less MAF molar fuel hydrogen asa function of MAF molar fuel oxygen; and so forth.

As used herein, the meaning of the words “using a genetics of the fossilfuel based on multi-variant analysis” is defined as using theinformation gathered from Eqs. (61), (62), (63), and (71) combined with(72), particular to a collection of fossil fuels of interest. Saidinformation may be used to form one or more required equations used by amatrix solution to resolve fuel chemistry. Said data, and useable data,is found in TABLE 2, TABLE 3, TABLE 4, TABLE 7 and TABLE 8. Thisdefinition does not mean that all equations must be employed. Forexample, Eq. (72) after combining with Eq. (71) to form a re-ordered Eq.(74), is applied using the data found in TABLE 7 and TABLE 8; becomingequation #1 in the 5×5 matrix solution. See the section entitledDETERMINING THE COMPLETE AS-FIRED FUEL CHEMISTRY. Eq. (63) is appliedusing the data found in TABLE 4, re-ordered as Eq. (64); becomingequation #2 in the 5×5 matrix solution. In the 5×5 matrix solution thereis no other information extracted from Eqs. (61), (62), (63), (71) or(72) which is required. The meaning of the words “developing a geneticsof the fossil fuel based on multi-variant analysis” is defined ascreating multi-variant relationships based on the general teachings ofthis invention, taken in the broadest interpretation of the inventivefeatures discussed in this paragraph and elsewhere herein. For example,these teachings are not limited to multi-variant analysis involving onlytwo elements; more than two may apply as would be applicable toequations of the form found in Eqs. (61), (62), (63) and (72).

As used herein, the meaning of the words “complete As-Fired fuelchemistry” is defined as comprising the following constituents of afossil fuel: elemental carbon, elemental hydrogen, elemental oxygen,elemental sulfur, elemental nitrogen, mineral matter (ash), and water.It is understood by one skilled in the art that elemental hydrogen andelemental oxygen derive from the dry chemical make-up of the fossil fuel(water free) and are not influenced by the fuel's water content Oftenfuel water is termed “fuel moisture”; they mean the same. Fuel mineralmatter is also termed “fuel ash”; they mean the same. Correctly stated,fuel ash is residue remaining after the combustion of a fossil fuel,commonly assumed to be the non-combustible mineral matter associatedwith the un-combusted fuel. The term “fuel ash” is commonly used in theindustry, meaning mineral matter, and is employed herein. As used hereinthe terms “Ultimate Analysis” or “Ultimate Analyses” meaning multipleUltimate Analysis, is defined as comprising the following constituentsof a fossil fuel: elemental carbon, elemental hydrogen, elementaloxygen, elemental sulfur and elemental nitrogen. As strictly defined, anUltimate Analysis is free of fuel gaseous components, free of fuel ashand free of fuel water; it truly represents Moisture-Ash-Gas-Free (MAGF)elemental constituents. For this disclosure, fuel gaseous components arenot considered, they are considered however in '994, whose teachings ofthese terms, and other minor components of a fossil fuel, may beincorporated herein for expansion of the disclosure's methods byfollowing the teachings found in '994. Note that an “As-Fired” conditionrefers to the actual fuel, with mineral matter and wet with water, inthe state of being fired into the thermal system; that is, fuel 22crossing the thermodynamic boundary 44 in FIG. 19.

As used herein, the words “operating a programmed computer” or“operating the programmed computer” are defined as the actionencompassing either to directly operate a programmed computer, to causethe operation of a programmed computer, or to authorize the operation ofa programmed computer at a facility controlled by the authorizer. Inlike manner, the word “calculating”, for example in the context of“calculating a fuel calorific value” is defined as encompassing eitherto engage directly in the action of calculating, or to cause acalculating process through a programmed computer, or to authorizecalculating process through a programmed computer at a facilitycontrolled by the authorizer.

As used herein, the words “calorific value” and “heating value” mean thesame. As used herein, the words “gross calorific value” and “higherheating value” mean the same. As used herein, the words “net calorificvalue” and “lower heating value” mean the same.

As used herein, the words “R² value” or “R² values” mean the Coefficientof Determination as computed by the Excel computer program using linearregression.

As used herein, the meaning of the word “quantifying” in the context of“quantifying the operation of a thermal system” is taken in the usualdictionary sense, meaning “to determine or express the quantity of . . .”; for example, at a minimum what is being “quantified” is a completeAs-Fired fuel chemistry.

System Stoichiometrics

Any study of the combustion of fossil fuels necessitates the formulationand use of a combustion equation. Combustion equations used by severalInput/Loss methods are described in '994 by its designated Eq. (29), in'429 by its Eq. (19), in '877 by its Eq. (19-corr), in US2004/128111 byits Eq. (19BL). These combustion equations are cited to demonstrate theflexibility of the present invention to different situations. Asexamples: consideration of CaO as an ash constituent (termed α_(CaCO3)),deriving from limestone found in the originating mineral matter istaught in '877 by its Eq. (19-corr); the study of black liquor fuelconsisting of hydrocarbons and sodium compounds is taught inUS2004/128111; and other variations are taught in the cited patentssupporting The Input/Loss Method. This invention's methods are taughtthrough a combustion equation defined by Eq. (29F) herein. Through Eq.(29F) stoichiometric terms become self-defined. Eq. (29F)'s nomenclatureis unique in that brackets are used for clarity: for example, theexpression “xα2[H₂O]” means the moles of fuel water/base, algebraicallysimply xα₁; the expression “d_(Act)[CO₂]” means the effluent moles ofcarbon dioxide/base, algebraically simply d_(Act); “βb_(A)[H₂O]” meansthe effluent moles of moisture found in the leakage air; etc. Thestoichiometric base of Eq. (29F) is 100 moles of dry Stack gas (i.e., atthe thermodynamic boundary). $\begin{matrix}\begin{matrix}\begin{matrix}\begin{matrix}\begin{matrix}\begin{matrix}\begin{matrix}\begin{matrix}\begin{matrix}\begin{matrix}{x\left\lbrack {{\alpha_{1}\left\lbrack N_{2} \right\rbrack} + {\alpha_{2}\left\lbrack {H_{2}O} \right\rbrack} + {\alpha_{3}\left\lbrack O_{2} \right\rbrack} + {\alpha_{4}\lbrack C\rbrack} +} \right.} \\{\left. {{\alpha_{5}\left\lbrack H_{2} \right\rbrack} + {\alpha_{6}\lbrack S\rbrack} + {\alpha_{10}\lbrack{ash}\rbrack}} \right\rbrack_{{As}\text{-}{Fired}\quad{Fuel}} +}\end{matrix} \\{{b_{Z}\left\lbrack {H_{2}O} \right\rbrack}_{\text{In-Leakage}} + \left\lbrack {\left( {1.0 + \beta} \right)\left( {{a\left\lbrack O_{2} \right\rbrack} + {a\quad{\varphi_{Act}\left\lbrack N_{2} \right\rbrack}} +} \right.} \right.}\end{matrix} \\{{\left. \left. {b_{A}\left\lbrack {H_{2}O} \right\rbrack} \right) \right\rbrack_{Air} + \left\lbrack {\left( {1.0 + \gamma} \right){b_{PLS}\left\lbrack \left( {{Ca}{CO}} \right)_{3} \right\rbrack}} \right\rbrack_{\text{As-Fired~~~PLS}}} =}\end{matrix} \\{{d_{Act}\left\lbrack {CO}_{2} \right\rbrack} + {g\left\lbrack O_{2} \right\rbrack} + {h\left\lbrack N_{2} \right\rbrack} +}\end{matrix} \\{{j\left\lbrack {H_{2}O} \right\rbrack} + {k_{Act}\left\lbrack {SO}_{2} \right\rbrack}_{Effluent} + {r\left\lbrack {SO}_{2} \right\rbrack}_{Capture} +}\end{matrix} \\\left\lbrack {{e_{Act}\lbrack{CO}\rbrack} + {f\left\lbrack H_{2} \right\rbrack} + {l\left\lbrack {SO}_{3} \right\rbrack} + {m\lbrack{NO}\rbrack} +} \right.\end{matrix} \\{{p\left\lbrack {N_{2}O} \right\rbrack} + {q\left\lbrack {NO}_{2} \right\rbrack} + {t\left\lbrack {C_{{YP}1}H_{{ZP}1}} \right\rbrack} +}\end{matrix} \\{\left. {u\left\lbrack {C_{{YP}2}H_{{ZP}2}} \right\rbrack} \right\rbrack_{{Minor}\quad{Components}} + {{xa}_{10}\lbrack{ash}\rbrack} +}\end{matrix} \\\begin{matrix}\begin{matrix}{{\sigma\quad{b_{PLS}\left\lbrack {{\left( {{Ca}{SO}} \right)_{4} \cdot {zH}_{2}}O} \right\rbrack}} +} \\\left\lbrack {\left\{ {\left( {1.0 - \sigma + \gamma} \right){b_{PLS}\lbrack{CaO}\rbrack}} \right\rbrack_{{Excess}\quad{PLS}} + {v\left\lbrack C_{Refuse} \right\rbrack} +} \right.\end{matrix} \\{{w\left\lbrack C_{Reject} \right\rbrack} + \left\lbrack {{\beta\quad{a\left\lbrack O_{2} \right\rbrack}} + {\beta\quad a\quad{\varphi_{Act}\left\lbrack N_{2} \right\rbrack}} + {\beta\quad{b_{A}\left\lbrack {H_{2}O} \right\rbrack}}} \right\rbrack_{{Air}\quad{Leakage}}}\end{matrix}\end{matrix} & \left( {29F} \right)\end{matrix}$

Resolution of Eq. (29F) is had when all n_(i) and n_(ii) quantities havebeen determined. Minor component terms of Eq. (29F) are typicallyresolved either through direct measurement (e.g., for CO and NO), orassume zero values, or through obtained relationships. All minorcomponents typically have only low parts-per-million concentrations andthus have little impact. Although non-traditional fuel components suchas α₀[C_(YR)H_(ZR)], α₇[CO₂], α₈[CO] and α₉[H₂S] are not presented inEq. (29F); treatment of such components is taught in '994 and whoseteachings of these terms may be directly transferred. Note that the termα₀[C_(YR)H_(ZR)] represents a composite gaseous fuel which may be usedfor flame stability, as sometimes employed when firing with coal. Asdefined herein the principle unknown fuel constituents, resolved by thisinvention, include those indicated in Eq. (29F) as: α₁[N₂], α₂[H₂O],α₃[O₂], α₄[α], α₅[H₂], α₆[S] and α₁₀[ash]. The minor effluents,e_(Act)[CO], f[H₂], l[SO₃], m[NO], p[N₂O], q[NO₂], t[C_(YP1)H_(ZP1)] andu[C_(YP2)H_(ZP2)] are presented for generalized teaching; their valuesare assumed to be constant or otherwise obtained. More specifically,many times effluent CO is measured, NO_(x) is measured generically thendivided into NO, N₂O and NO₂ compounds based on estimation or periodicmeasurements. The unburned hydrocarbons C_(YP1)H_(ZP1) andC_(YP2)H_(ZP2) represent compounds which could be measured withhydrocarbon (combustibles) instrumentation, or otherwise obtained. Thetrue importance and functionality of Eq. (29F) to The Input/Loss Method,or any other combustion equation used for any of the Input/Loss methods,lies in the fact that consistency of molar balances is required forsuccessful system understanding, for conservation of mass flows and forresolution of fuel chemistry. For clarity the following major terms areassociated with system stoichiometrics of Eq. (29F):

-   -   Total effluent (boundary) water≡J_(Act)=j+b_(A)β    -   Boiler oxygen before air leakage (termed g′_(Act))≡gR_(Act)    -   Total effluent (boundary) oxygen≡G_(Act)=g+aβ    -   Total effluent (boundary) carbon dioxide≡d_(Act)    -   Total effluents referenced to the        boundary=Σn_(i)+Σ_(nii)+β(a+aφ_(Act)+b_(A))    -   Total effluents before air leakage, referenced upstream of the        air in-leakage=R_(Act)Σn_(i)+R_(Act)Σn_(ii)    -   Dry combustion air without air leakage referenced to the        boundary=(a+aφ_(Act))    -   Wet combustion air without air leakage referenced to the        boundary=(a+aφ_(Act)+b_(A))    -   Dry air from air leakage found at the boundary=β(a+aφ_(AcT))    -   Total in-flow of wet combustion air and wet air leakage found at        the boundary=(1.0+β)(a+aφ_(Act)+b_(A)).

Eq. (29F) describes at least three features of critical importance whendetermining fuel chemistry using one of the Input/Loss methods. Thecritical features include: 1) its ability to address air pre-heaterleakage through application of the Air Pre-Heater Leakage Factor,R_(Act), and through the Air Pre-Heater Dilution Factor, β; 2) theability to describe effluent concentrations on either side of the airpre-heater, again through application of R_(Act); and 3) the use of anexplicit φ_(Act) term allowing for variable O₂ concentration in thesystem's local combustion air. Air pre-heater leakage dilutes allcombustion effluents with moist air from the local environment, thus allimportant effluents H₂O, CO₂ and O₂ used for this invention are altered.Furthermore, many times, although not always, a power plant's moreprecise effluent measurements may be found on the air pre-heater's inlet(economizer outlet or Boiler), and not at the air heater outlet (orStack); refer to FIG. 19. Although most environmental regulationsrequire effluent measurements at the system's boundary, translationbetween the air heater inlet to outlet measurements is many timesessential. Eq. (29F) allows for such taanslation through the R_(Act)term, defined above such that 100 moles of dry gas are computed both atthe upstream and downstream locations of the air pre-heater; see“Boiler” of FIG. 19. Thus effluents may be used by the present inventioneither upstream or downstream of the air pre-heater; refer to theG_(Act) and J_(Act) terms defined above, allowing conversion betweenmeasurements with and without air leakage. For example, combustion gasconditions for oxygen and water upstream of the air pre-heater and afterexiting the heat exchanger/combustion region, see FIG. 19, would employthe terms: gR_(Act) and jR_(Act). That is, one would actually measure agR_(Act) moles of dry O₂ upstream of the air pre-heater and afterexiting the heat exchanger/combustion region as based on 100 moles ofdry gas found at that location. Combustion gases downstream of the airpre-heater typically exit the system to the environment (i.e., Stack),in other words the gaseous effluent boundary of the system (100 moles ofdry gas at the Stack includes air leakage). If limestone is injectedinto the combustion process to control effluent SO₂ it will createadditional effluent CO₂; further, it could decrease the effluent H₂O ifthe sulfate product is matrixed with water, CaSO₄-zH₂O. Thus sucheffects must be considered. Of course CO₂, H₂O and O₂ are threeimportant effluents to the present invention. In addition to the basicstoichiometrics afforded, Eq. (29F) allows numerous and obviousdeterminations of molar and mass ratios.

Based on these teachings, the following further explains the importanceof the Air Pre-Heater Leakage Factor, R_(Act), and the Air Pre-HeaterDilution Factor, β, their definitions and developments and use. Considerthat air in-leakage associated with a fossil-fired system, and ascommonly associated with in-leakage at the system's air pre-heater, isdefined by the American Society of Mechanical Engineers' PerformanceTest Code 4.3 (1974) as the mass of moist air leakage divided by themass of wet combustion gas entering the air pre-heater. The wetcombustion gas is taken at the gas inlet of the air pre-heater (i.e.,Boiler, or economizer outlet before the air pre-heater). That is, asdefined herein using Eq. (29F) nomenclature, noting that 100 moles ofdry gas is the bases at the Boiler, is given by: $\begin{matrix}{{{Wet}\quad{APH}\quad{Leakage}} \equiv \frac{R_{Act}{\beta\left( {a + {a\quad\varphi_{Act}} + b_{A}} \right)}N_{MoistAir}}{\left( {100 + {R_{Act}j}} \right)N_{WetGas}}} & (20)\end{matrix}$where, as defined above:

R_(Act)=(Moles of CO₂ entering the air pre-heater)/(Moles of CO₂ leavingthe air pre-heater). The expression for R_(Act) is equivalent to (Molesof Boiler CO₂) divided by (Moles of Stack CO₂), noting that each ofthese would-be measurements is referenced to 100 moles of dry gas. TheAir Pre-Heater Dilution Factor is then developed by performing a totaldry gaseous effluent molar balance at the Stack, see FIG. 19:100 moles dry gaseous effluent at Stack=Σn _(i)+β(a+aφ _(Act))  (21)and then solving for β: β=(100−Σn_(i))/(a+aφ_(Act)). The stoichiometricbase of Eq. (29F) implies that 100 moles of dry gaseous effluentupstream of the air pre-heater (Boiler) is given by R_(Act)Σn_(i) (thusΣn_(i)=100/R_(Act)); therefore: $\begin{matrix}{\beta = {{\left( {100 - {100/R_{Act}}} \right)/\left\lbrack {a\left( {1.0 + \varphi_{Act}} \right)} \right\rbrack} \equiv {100{\left( {R_{Act} - 1.0} \right)/{\left\lbrack {R_{Act}{a\left( {1.0 + \varphi_{Act}} \right)}} \right\rbrack.}}}}} & (22)\end{matrix}$If, instead of obtaining the ratio of CO₂ across the air pre-heater, theratio of O₂ is obtained, the following may then be developed:R′ _(Act)=(Moles of O₂ entering the air pre-heater)/(Moles of O₂ leavingthe air pre-heater).where, converting from R′_(Act) to R_(Act), using algebraicmanipulations results in, when measuring Stack O₂ (the term G_(Act)):$\begin{matrix}{R_{Act} \equiv \frac{100 - {R_{Act}^{\prime}{G_{Act}\left( {1.0 + \varphi_{Act}} \right)}}}{100 - {G_{Act}\left( {1.0 + \varphi_{act}} \right)}}} & (23)\end{matrix}$If measuring Boiler O₂ (for Eq. (24) termed g′_(Act)): $\begin{matrix}{R_{Act} \equiv \frac{{100R_{Act}^{\prime}} - {R_{Act}^{\prime}{g_{Act}^{\prime}\left( {1.0 + \varphi_{Act}} \right)}}}{{100R_{Act}^{\prime}} - {g_{Act}^{\prime}\left( {1.0 + \varphi_{Act}} \right)}}} & (24)\end{matrix}$There are, of course, a number of variations to these formulations, suchas employing 100 moles of wet effluents at the Stack, thus replacing Eq.(21) with:100 moles wet effluent at Stack=(Σn _(i) +j)+β(a+aφ _(Act) +b_(A))  (25)or using an oxygen base for the wet effluents at the Stack, thus:(Σn_(i)+J_(Act))/a+β(1.0+φ_(Act)); or using a combustion equation whichis based on a mole of fuel carbon (xα₄); etc. What is important to thisinvention, important to The Input/Loss Method, and important to any ofthe Input/Loss methods, is that the Air Pre-Heater Leakage Factor(R_(Act)) allows gaseous measurements to be employed on either side ofthe system air in-leakage. Typically, but not always, O₂ is measured inthe combustion gas stream inlet to the air pre-heater (Boiler), whileCO₂ is measured at the Stack (downstream from the air pre-heater).

After establishing system stoichiometrics, the next stage of the processinvolves the recognition that because a given fuel has an unique,although unknown, chemical composition, when burned it will yield uniqueconcentrations of principle effluents CO₂, H₂O, O₂, and SO₂ (if fuelsulfur is present). The gaseous effluent concentrations are used tocompute the fuel chemistry, with this chemistry fuel calorific value andboiler efficiency are then computed, in turn this information allows thecomputation of fuel flow and system efficiency. The gaseous effluentsfrom any fossil combustion process are N₂, CO₂, H₂O, O₂ and SO₂ (if fuelsulfur is present). H₂O, when effluent from combustion, is in itssuperheated phase, thus acting as a gas. The source of N₂ is principallythe air used to burn the fuel and has little chemical reactiveness, thusits sensitivity to the fuel's chemical composition is not significant.The use of a measured effluent N₂ is not considered practical, nor canadd to the matrix solution, given that fuel nitrogen is generally one ofthe smallest components of a fossil fuel, effluent N₂ being the largestproduct, thus even the slightest measurement error would have anenormous influence on computed fuel chemistry. SO₂ effluentconcentrations are generally in the parts per million thus its impactmay have minor importance, but not always.

As an intrinsic chemical relationship, the relative concentrations ofcarbon (α₄), hydrogen (α₅) and oxygen (α₃) found in any fossil fuel willhave significant impact on the relative concentrations of CO₂, H₂O andO₂ found in the effluent. The concept of involving fuel oxygen in thisstatement is fundamentally different from '994. Considered whendeveloping this invention was an “Oxy-Hydrocarbon” (OHC) approach tostoichiometrics—not a simple “hydrocarbon” approach—and this beingpossible only through multi-variant analysis of fossil fuels (explainedbelow). The CO₂, H₂O and O₂ effluents will be influenced by thefollowing: O₂ used to burn the fuel (i.e., the Air/Fuel ratio); fuelwater, α₂; in-leakage of water including tube leaks (b_(Z)); and waterin the combustion air (b_(A)). This implies that the molar fractions ofCO₂, H₂O and O₂ present in the effluent (the system's boundary, i.e.,data at the Stack or data translated from air pre-heater inlet to theStack) must be unique relative to the supplied fuel and suppliedcombustion air.

The following elemental molar balances may be derived from thecombustion equation, Eq. (29F). The Γ_(k) expressions are simplyconvenient groupings of quantities, principally comprising measuredeffluents (known values) which have the greatest influence on theindividual fuel elements of interest. Many coal-fired units usesupplementary firing with gaseous fuel or fuel oil. Such minor fuelterms, e.g., composite gaseous fuels described by α₀[C_(YR)H_(ZR)], notshown in Eq. (29F) but taught in '994, may be included within Γ_(k)expressions and are multiplied, initially, by an estimated fuel moles,x_(MAF). Such minor terms may be quickly resolved when converging onx_(MAF). Given these groupings, the Γ_(k) expressions of Eqs. (36)through (41), with solution of the moles of combustion oxygen (the term“a”) as discussed below, may be treated as known quantities. Theelemental wet fuel components are considered unknowns, as are the fuelmoles; the unknowns include the following: α₁, α₂, α₃, α₄, α₅, α₆, α₁₀and “x” in Eq. (29F). $\begin{matrix}{{x\quad\alpha_{1}} = {\Gamma_{N2} - {a\quad\varphi_{Act}}}} & (30) \\{{x\left( {\alpha_{5} + \alpha_{2}} \right)} = \Gamma_{H2O}} & (31) \\{{x\left( {\alpha_{3} + {\alpha_{2}/2}} \right)} = \Gamma_{O2}} & (32) \\{{x\quad\alpha_{4}} = \Gamma_{CO2}} & (33) \\{{{x\quad\alpha_{6}} = \Gamma_{SO2}}{{where}:}} & (34) \\{\Gamma_{N2} = {100 - \left( {d_{Act} + e_{Act} + f + G_{Act} + k_{Act} + l + {m/2} + {q/2} + t + u} \right) - {100{{\varphi_{Act}\left( {R_{Act} - 1.0} \right)}/\left\lbrack {R_{Act}\left( {\varphi_{Act} + 1.0} \right)} \right\rbrack}}}} & (36) \\{\Gamma_{H2O} = {\left( {J_{Act} - {b_{A}\beta}} \right) + f + {\left( {{ZP}1} \right){t/2}} + {\left( {{ZP}2} \right){u/2}} - b_{Z} - b_{A} + {b_{PLZ}\sigma\quad z}}} & (37) \\{\Gamma_{O2} = {d_{Act} + {e_{Act}/2} + \left( {G_{Act} - {a\quad\beta}} \right) + {\left( {J_{Act} - {b_{A}\beta}} \right)/2} + {m/2} + {p/2} + q - a - {b_{A}/2} - {b_{Z}/2} + k_{Act} + {3{l/2}} + r + {\left( {{3\sigma} - 2 - {2\gamma} + {\sigma\quad z}} \right){b_{PLS}/2}}}} & (38) \\{\Gamma_{OHS} = {d_{Act} + {e_{Act}/2} + \left( {G_{Act} - {a\quad\beta}} \right) + {\left( {J_{Act} - {b_{A}\beta}} \right)/2} + {m/2} + {p/2} + q - a - {b_{A}/2} - {b_{Z}/2}}} & (39) \\{\Gamma_{CO2} = {d_{Act} + e_{Act} + {\left( {{YP}1} \right)t} + {\left( {{YP}2} \right)u} + v + w - {\left( {1.0 + \gamma} \right)b_{PLS}}}} & (40) \\{\Gamma_{SO2} = {\left( {{\sigma\quad b_{PLS}} + {k_{Act}/\Gamma_{ESP}}} \right)\left\lbrack {1.0 + {\Gamma_{SO3}/\left( {1.0 - \Gamma_{SO3}} \right)}} \right\rbrack}} & (41)\end{matrix}$In these relationships the subscript “Act” means an effluent measurementor assumption (an “actual” value). The term J_(Act) in Eqs. (37), (38)and (39) relating to the moles of effluent H₂O could be input as aconstant value or measured or otherwise obtained. All other values inEqs. (36) through (41) are either measured, evaluated explicitly basedon input data, internal models and/or have minor import but are carriedin the formulations for teaching consistency of stoichiometrics.

Eq. (29F) teaches that fuel sulfur is allowed to produce both SO₂ andSO₃. For the SO₂ produced from fuel sulfur a portion is allowed to becaptured by effluent ash or converted by limestone. The followingrelationships explain, resulting in Eq. (41); refer to the DEFINITIONSsection above for meanings of the variables employed in Eq. (42). From asimple sulfur balance using Eq. (29F): $\begin{matrix}{{\Gamma_{SO2} = {{x\alpha}_{6} = {k_{Act} + l + r + {\sigma\quad b_{PLS}}}}}{{{where}:{x\alpha}_{6}} = {k_{F} + l}}{k_{F} = {k_{Act} + r + b_{PLS}}}{{k_{Act} + r} = {k_{Act}/\Gamma_{ESP}}}{l = {{k_{F}{\Gamma_{SO3}/\left( {1.0 - \Gamma_{SO3}} \right)}} = {\left( {{\sigma\quad b_{PLS}} + {k_{Act}/\Gamma_{ESP}}} \right){\Gamma_{SO3}/\left( {1.0 - \Gamma_{SO3}} \right)}}}}} & (42)\end{matrix}$Therefore by reducing Eq. (42) using the above relationships, Eq. (41)results, it employing either known quantities, or measurable quantitiesor quantities which may be reasonably estimated knowing the particularthermal system. It will become apparent that prior methods as taught in'994, where fuel sulfur may have been assumed constant, are not adequatefor the present invention. When sulfur is present in the fuel, thegenetics of the fossil fuel allow its explicit computation.

As a group, these relationships are of critical importance forunderstanding The Input/Loss Method. If fuel chemistry is to beresolved, thus calorific value, boiler efficiency, accurate fuel flowand system efficiency, then stoichiometric relationships generallyrepresented by Eqs. (30) to (41) must be resolved. These equations arenot unique in their grouping of terms; further reductions and/orcomplexities are certainty possible. The grouping of terms adopted hereprincipally follows from the right-side of Eq. (29F).

Eqs. (30) through (34) yield five equations with nine unknowns. For thissituation, unknowns include α₁ through α₆, α₁₀, and the terms “a” and“x”. The term “x” is a convenience term and could be divided throughchanging the base of Eq. (29F) to unity moles of fuel, thus eliminatinguse of xα_(j) terms comprising two unknowns. However, if done, then theeffluent's base becomes per mole of fuel, e.g., thus an effluent termd_(Act)/x, adding a different complexity involving the normalization ofeffluent measurements. Although the requirement Σα_(MAF-j)=1.00 is aconvenience, it affords another, and viable, equation. By making a molarnitrogen balance, and assuming 100 moles of dry gaseous effluent at theboundary, the “a” quantity (moles of combustion oxygen) may be resolvedindependent of Eq. (30), thus reducing the unknowns; detailed below.Again, the entire combustion equation, Eq. (29F), could be dividedthrough by α₄, or xα₄, thus setting a carbon base. Effluent N₂ could beresolved by difference assuming 100 moles of gaseous effluent (CO₂, H₂O,O₂, SO₂, the minor pollutants being measured or assumed), or N₂ could bemeasured directly. However, using effluent N₂ to resolve fuel nitrogen,al, is not practical given fuel nitrogen is typically a minor fuelconstituent (as is sulfur), any error made in measuring effluent N₂would greatly effect all fuel constituents; it is not a practicalequation. Or, further still, by assuming constant values for fuelnitrogen and sulfur, α₁ and α₆, with resolution of “a”, and say:α₃=1.0−Σα_(MAF-j), j≠3, the system is reduced to three equations withfour unknowns; these include Eqs. (31) through (33), with α₂, α₄, α₅ and“x”. As another example, if α₃ is assumed constant, then the combinedEqs. (31) and (32) (with cancellation of xα₂) represents one equationwith two unknowns, “x” and α₅. And, of course, further reductions andmanipulations of unknowns and equations is entirely possible. However,the point is that close examination of the physical problem ofcombustion stoichiometrics, in which fuel chemistry is to be determinedfrom effluents, indicates that the mathematical system has more unknownsthan equations. In summary, these manipulations are discussed toemphasize that, as taught by this invention, a new approach must beprovided which provides, not mere simple correlations of hydrogen versuscarbon as was done in '994, but rather establishing the genetics of thefossil fuel. '994 solution employed, that was believed to be intrinsicchemical relationships, correlation constants within the resolution ofthe combustion equation (i.e., single-variant correlation constantsappear within stoichiometric equations). Although '994 employedsingle-variant correlations based on MAF molar concentrations,single-variant correlations based on weight concentrations are commonlyfound throughout the fossil fuel literature.

To address the solution problem, whereas the '994 solution was achievedthrough relationships found between MAF molar fuel hydrogen and MAFmolar fuel carbon (and representing a particular mined fuel), thepresent invention recognizes the genetics of the fossil fuel and employsits findings to achieve a matrix solution. The Preferred Embodiment doesnot require that the minor fuel constituents be assumed constant, theymay be measured quantities (e.g., effluent SO₂, effluent CO, effluentNO_(X), etc.) and/or otherwise obtained. Further, as will becomeapparent, the Preferred Embodiment allows use of multidimensionalminimization techniques taught in '877 which addresses instrumentationerrors.

Returning to the solution problem as posed by Eq. (29F), the problem issolved, in part, by reducing α_(j) quantities to a MAF molar basis,eliminating the influence of the two components not chemically involvedwith the Oxy-Hydrocarbon fuel per se, water and mineral matter (ash).Before addressing the genetics of fossil fuels, the following teacheshow fuel water and fuel ash are resolved, the α_(MAF-i) terms requiredare then fully taught in subsequent sections. MAF molar fuel water isresolved by adding Eqs. (31) and (32), then substituting x_(MAF) forΓ_(CO2)/α_(MAF-4); see Eq. (92):α_(MAF-2)=2[α_(MAF-4)(Γ_(H2O)+Γ_(O2))/Γ_(CO2)−α_(MAF-5)−α_(MAF-3)]/3  (42)

To determine fuel ash using explicit relationships requires examinationof the total system. The only system effect of fuel ash is as a puredilutive or concentrative influence on fuel, and of course on the fuel'scalorific value. From a qualitative viewpoint, as fuel ash increases atthe expense of carbon (for example), the amount of combustion airrequired to produce the same effluent O₂ actually increases given thatmore fuel is required to achieve the same energy flow to the workingfluid given less combustibles in the fuel; in large commercial powerplants the coal is borne by combustion air to the furnace region. Givena decreasing calorific value (higher ash) increased fuel flow isrequired to meet the same energy flow to the working fluid. Thus anideal system parameter for such sensitivities, which is routinelymeasured at fossil-fueled systems, is the indicated Air/Fuel ratio.Generally such sensitivities are reasonable, a 10 percent increase inash for a common coal will cause a linear effect in the Air/Fuel ratio.The wet, mass base, Air/Fuel ratio (termed AF_(Act)), a calculationalquantity, is developed as follows:AF _(Act)=(m _(Air) +m _(Moisture))/m _(AF)  (48A)AF _(Act)=(1+β)[(a+aφ _(Act))N _(Air) +b _(A) N _(H2O)]/(xN_(AF))  (48B)Expanding the term xN_(AF) in Eq. (48B), noting that N_(AF) relates tothe wet As-Fired fuel (i.e., j=1, 2, 3, 4, 5, 6, 10):xN _(AF) =x(Σ_(j=1−6) N _(j)α_(j) +N _(j)α_(j) +N ₁₀α₁₀)  (49)and then employing the following definitions of MAF fuel moles and fuelconstituents:x _(MAF) ≡x/(1.0+α_(MAF-2)+α_(MAF-10))  (50)α_(MAF-j)≡α_(j)(1.0+α_(MAF-2)+α_(MAF-10))  (51)allows substitution of Eqs. (50) and (51) into Eq. (49) for x and a_(i),cancelling the term (1.0+α_(MAF-2)+α_(MAF-10)) as intended, and thensubstituting into Eq. (48B) yields a solvable form:xN _(AF) =x _(MAF)(Σ_(j=1−6) N _(j)α_(MAF-j) +N ₁₀α_(MAF-10))  (52)AF _(Act)=(1.0+β)[(a+aφ _(Act))N _(Air) +b _(A) N _(H2O) ]/[x_(MAF)(Σ_(j=1−6) N _(j)α_(MAF-j) +N ₁₀α_(MAF-10))]  (53)Simplifying Eq. (53) and solving for MAF fuel ash, α_(MAF-10), yieldsthe following results. Note in Eq. (54) that a normalized Air/Fuel ratiois used, becoming AF_(Act), normalized to indicated plant data, definedby Eq. (57). x_(MAF) is substituted using Eq. (56).α_(MAF-10)=[Γ_(Ash)α_(MAF-4)/(Γ_(CO2) N ₁₀)]−Σ_(j=1−6) N _(j)α_(MAF-j)/N ₁₀  (54)where:Γ_(Ash)≡(1.0+β)[(a+aφ _(Act))N _(Air) +b _(A) N _(H2O) ]/AF _(Act)  (55)x _(MAF)=Γ_(CO2)/α_(MAF-4)  (56)AF _(Act) ≡AF _(input)(AF _(Ref1) /AF _(Ref2))  (57)a=(Γ_(N2) −x _(MAF)α_(MAF-1))/φ_(Act)  (58)The variable AF_(input) is the wet Air/Fuel ratio from the system's datacollection device (an indicated value); the ratio (AF_(Ref1)/AF_(Ref2))is used to scale AF_(input). The value of N₁₀ in Eq. (54) is input as aconstant, or fitted as a function of α_(MAF-10) (thus solving aquadratic equation), or fitted as a function of HHV_(MAF). Note that asystem's indicated plant fuel flow measurement could obviously be usedin place of AF_(Act), applying similar techniques as demonstrated indetermining α_(MAF-10). However, use of an AF_(Act) variable ispreferred since it integrally involves effluent and combustion air terms(through Γ_(CO2), Γ_(N2) and Γ_(Ash)), and thus through suchdependencies allows error analysis techniques to be operational andpractical. It is noteworthy that the explicit procedure of determiningfuel ash, and through use of the term (1.0+α_(MAF-2)+α_(MAF-10)) of Eqs.(50) and (51), allows any errors made in fuel water, α_(MAF-2), to beoff-set by fuel ash, α_(MAF-10). This must occur since any givenquantity xα_(j) (wet-base) must be equivalent to x_(MAF)α_(MAF-j)(MAF-base); if not, such wet to MAF conversions would numerically causeinconsistencies in the computed Air/Fuel ratio.

In summary, MAF fuel ash, α_(MAF-10), may be determined from theexplicit solution taught by Eq. (54). By “explicit solution” is meantthat only independent (known) variables appear on the right hand side ofan equation, including Eq. (54), the dependent term on the left (e.g.,the α_(MAF-10) term). However, if the typical fossil fuel has no, littleor essentially constant fuel ash, then α_(MAF-10) may be held constant,including zero. Further, it has been found that for certain lignitefuels, fuel ash may be determined by knowing, or estimating, MAFcalorific value. For Greek lignite and lignite A, the following has beenfound broadly descriptive:α_(MAF-10)=0.4534−1.5199×10⁻⁵ HHV _(MAF-EST); for kJ/kg  (60A)α_(MAF-10)=0.4534−3.5352×10⁻⁵ HHV _(MAF-EST); for Btu/lbm  (60B)The estimated MAF calorific value, HHV_(MAF-EST), may be reasonablyconstant especially for the poorer fuels, eliminating iterativeprocedures. On the other hand, the MAF molar fuel ash value for thepoorer quality fuels has been found to be remarkably constant. Inaddition, as taught in '994, fuel ash instruments are available whichdetermine on a dry basis the concentration of fuel ash. Thus a fuel ashconcentration may be selected from the group consisting of: a constantvalue of fuel ash, a predictable value of fuel ash, a measured value offuel ash determined from a fuel ash instrument and a value of fuel ashdetermined from explicit solution, as an obtained fuel ashconcentration. The Preferred Embodiment is to determine MAF molar fuelash from the explicit solution, Eq. (54). If however data required forEq. (54) is missing, or fuel ash is not sufficiently variable, then thereasonable Preferred Embodiment is to hold MAF molar fuel ash constant.

As taught in the above three paragraphs, fuel water and fuel ash may beexplicitly determined provided the MAF fuel chemistry is known, that isknown α_(MAF-1), α_(MAF-3), α_(MAF-4), α_(MAF-5) and α_(MAF-6). Fuelwater is dependent on α_(MAF-4), α_(MAF-5) and α_(MAF-3). Fuel ash, ifdetermined using Eq. (54), is dependent on all fuel constituents lessash, including α_(MAF-2) of Eq. (42), “a” of Eq. (58), x_(MAF), etc. asindicated. The following section teaches the genetics of fossil fuels,through which the complete fuel chemistry is resolved. Note that if theminor fuel constituents of sulfur, nitrogen and ash can be assumedconstant (including zero), then the matrix solution need only considerMAF molar fuel oxygen, carbon and hydrogen; thus an Oxy-Hydrocarbonunderstanding of the fuel.

Genetics of Fossil Fuels

The teachings of '994 relied on simple single-variant correlations toprovide missing equations. As discussed above, single-variantcorrelations have been shown, for many important fuels, as not beingadequate. What was discovered using Irish peat data (having significantfuel oxygen), was that multi-variant analysis not only dramaticallyimproved R² values, but improved R² values to the point that a baseunderstanding of the genetics of fossil fuels is obtained. What wasdiscovered was that the following multi-variant relationships have aprofound ability to describe fossil fuels with unheard of accuracy; anaccuracy which addresses the very genetics of fossil fuels.α_(MAF-4)+α_(MAF-5) =J _(OHC1) +K _(OHC1)α_(MAF-3)  (61)α_(MAF-4)+α_(MAF-3) =J _(OHC2) +K _(OHC2)α_(MAF-5)  (62)α_(MAF-5)+α_(MAF-3) =J _(OHC3) +K _(OHC3)α_(MAF-4)  (63)In these relationships, fuel hydrogen is taken in the diatomic form(H₂), as is fuel oxygen (O₂); as α_(MAF-5) and α_(MAF-3) result from Eq.(29F). This assumption, versus the monatomic, does not affect theoutcome. The predictability of Eq. (63) versus '994 technology is bestobserved by comparing the Irish peat of FIG. 1 to FIG. 2 results inimproving R² value from 65.90% to 98.45%. Comparing Powder River Basincoals of FIG. 3 to FIG. 4 results in improving R² value from 71.93% to99.77%. Comparing High Seas and similar high volatile coals of FIG. 5 toFIG. 6 results in improving R² value from 81.77% to 99.77%. Note thatthe Irish peat data was obtained from laboratory analyses taken over 42years; with a greater consistency of laboratory procedures, it isreasonable to assume that the R² value 98.45% for FIG. 2 would approachthose found for FIG. 4 and FIG. 6. Although the use of multi-variantanalysis may appear to be a simple extension of a single-variantapproach ('994), there was nothing found in the fossil fuel literaturewhich would suggest multi-variant analysis; and nothing found in theliterature which would suggest that resultant multi-variantrelationships, e.g., Eqs. (64) or (74), may be used to provide missingequations for matrix solutions to fuel chemistry.

The data of FIG. 5 (hvAb, hvBb, hvBc and spot High Seas data) is ofinterest given that the observed distribution of data about the linearmean is approximately uniform. FIG. 5 provides a statistical example inwhich the R² value computes artificially high. Using this as a “bestcase” of '994 methods, FIG. 7A over-plots on FIG. 5 data variance linesat ±3.116%. As observed, these variance lines essentially encompass thedata scatter. Establishing the variance lines, FIG. 7B then forms anartificial repeat of FIG. 5 & FIG. 7A but whose data is biased about themean such that Excel's R² value matches that of FIG. 5 & FIG. 7A. Thisis important for the FIG. 7B computed database then allows study ofother distributions, producing other variance lines and R² values. Oneof these, indicating a ±0.840% variance, yields an R² value of 98.45, isplotted offering visual understanding of what ≈98% predictabilityimplies. The quantified impact of these and other variances on TheInput/Loss Method's computed calorific value based on FIG. 5 data islisted in TABLE 1. The analysis associated with TABLE 1 assumes auniform distribution, thus the average error to be made in calorificvalue (CV) is taken as one-half of the full effect. Results indicatethat '994 technology clearly indicates unacceptable results when theequivalent error on effluent CO₂ is much greater than 1.0% (i.e., thedata of FIG. 5 having an R² value below 82% given a uniform distributionof variances). TABLE 1 also indicates that the effect on computed CV isacceptable when an R² value is found greater than 98%, a CV error of 263ΔkJ/kg (113 ΔBtu/lbm). This level of predictability agrees with thecommonly accepted error in measured CVs, determined between independentlaboratories testing the same fuel samples, at ±233 ΔkJ/kg or ±100ΔBtu/lbm. One can not ask more in understanding the genesis of fossilfuels than that associated with measurement uncertainty betweenlaboratories testing the same fuel. TABLE 1 Practical Impact of R² onThe Input/Loss Method Based on FIG. 5 Data Impact of Equation (from FIG.5): R² (%) ½ Variance Impact of Effluent CO₂ on Input/Loss Hyd =[−0.6294(Car) + 0.7054] Computed on Effluent As-Fired Calorific Value(CV), without (1.0 ± Var/100) by Excel CO₂ (%) Error Analysis or L₁₀Correction Variance = 0.000% 100.00 0.0000 none, CV = 29107.934 kJ/kg(12514.159 Btu/lbm) Variance = 0.840% 98.45 0.2720 0.90%, 263 ΔkJ/kg(113 ΔBtu/lbm) Variance = 1.556% 94.83 0.5040 1.65%, 481 ΔkJ/kg (207ΔBtu/lbm) Variance = 2.334% 88.98 0.7560 2.46%, 716 ΔkJ/kg (308ΔBtu/lbm) Variance = 3.116% 81.77 1.0095 3.26%, 948 ΔkJ/kg (408ΔBtu/lbm)

The predictability of these equations is seen in FIG. 8, FIG. 9 and FIG.10 for anthracite, semi-anthracite and sub-bituminous B. Thepredictability of these equations is also seen in FIG. 11, FIG. 12 andFIG. 13 for lignite A, Greek Lignite and Irish peat. The R² valuesassociated with these and other Ranks are presented in TABLE 2, TABLE 3and TABLE 4. Such predictability is of such reliability that any of theEqs. (61), (62) or (63) may be used in the matrix solution. Eq. (63) ischosen such that (α_(MAF-5)+α_(MAF-3)) was demonstrated as having nofunctionality with L₁₀ (explained below). In re-arranging terms, Eq.(63) becomes:α_(MAF-3) −K _(OHC3)α_(MAF4)+α_(MAF-5) =J _(OHC3)  (64) TABLE 2 MAFMolar Fuel Carbon + Diatomic Hydrogen vs MAF Molar Fuel Diatomic OxygenRank J_(OHC1) K_(OHC1) R² (%) anthracite (an) 0.994587 −1.029322 94.61semi-anthracite (sa) 0.992139 −0.927044 88.07 High Seas (hvAb, hvBb,spot) 0.991273 −0.968619 96.66 sub-bituminous A (sub A) 0.987991−0.917961 95.55 Powder River Basin 0.995394 −1.017100 98.99sub-bituminous B (sub B) 0.992029 −0.993473 95.75 sub-bituminous C (subC) 0.981005 −0.849783 88.78 lignite A (lig A) 0.986298 −0.919924 88.64Greek lignite 0.986963 −1.028534 97.45 Irish peat 0.984391 −0.94079894.18

TABLE 3 MAF Molar Fuel Carbon + Diatomic Oxygen vs MAF Molar FuelDiatomic Hydrogen Rank J_(OHC2) K_(OHC2) R² (%) anthracite (an) 0.994791−1.003952 99.74 semi-anthracite (sa) 0.993794 −1.004406 97.99 High Seas(hvAb, hvBb, spot) 0.982893 −0.966008 99.51 sub-bituminous A (sub A)0.994627 −1.008012 99.42 Powder River Basin 0.996057 −1.006130 99.73sub-bituminous B (sub B) 0.992464 −1.000103 99.33 sub-bituminous C (subC) 1.000139 −1.032331 98.55 lignite A (lig A) 1.000654 −1.031797 97.59Greek lignite 0.988563 −1.016521 97.23 Irish peat 0.971585 −0.93313497.19 Generic Non-Volatile (an, sa, 0.995497 −1.011011 99.95 sub A, subB, sub C, lig A)

TABLE 4 MAF Molar Fuel Diatomic Hydrogen + Diatomic Oxygen vs MAF MolarFuel Carbon Rank J_(OHC3) K_(OHC3) R² (%) anthracite (an) 0.989047−0.993931 99.80 semi-anthracite (sa) 0.986130 −0.991377 98.60 High Seas(hvAb, hvBb, spot) 1.007944 −1.022818 99.68 High Volatile (hvAb, hvBb,1.005030 −1.018692 99.77 hvCb, spot) sub-bituminous A (sub A) 0.990659−0.997212 99.50 Powder River Basin 0.986835 −0.988635 99.77sub-bituminous B (sub B) 0.989200 −0.995069 99.43 sub-bituminous C (subC) 0.971525 −0.969655 98.13 lignite A (lig A) 0.963022 −0.955311 96.97Greek lignite 0.971701 −0.978878 99.19 Irish peat 1.017332 −1.04562098.45

The consistency observed in the above TABLES is also observed in a widecollection of fuel samples, depending on which multi-variant analysis ischosen. FIG. 14 is a plot of MAF molar fuel carbon plus MAF molar fueldiatomic oxygen versus MAF molar fuel diatomic hydrogen using both thehighest and lowest energy fuels: anthracite (an), sem-anthracite (sa),sub-bituminous A (sub A), sub-bituminous B (sub B), sub-bituminous C(sub C) and lignite A (lig A). As observed, with an R² value of 99.95%(TABLE 3), such predictability portents further use of Eq. (62) thanjust providing a missing equation for The Input/Loss Method. Eq. (62)may be used to over-check Ultimate Analysis results for any fuel fallinginto these general Ranks. In essence, Eq. (61), (62) and (63) may beused as an over-check for data outliers. As seen with carefulobservation of FIG. 14, two or three of the sub C data may be classed asoutliers. What is being described through Eqs. (61), (62) and (63) isthe inherent carbon, hydrogen and oxygen make-up of a fossil fuel, itsOxy-Hydrocarbon construct. Indeed, it can be demonstrated as consistentat the MAF molar level. A general comparison of '994 methods and thoseadvocated by this invention is observed in TABLE 5. Note that all R²values for the present invention are greater than 98% except lignite A.Such genesis is simply not seen with single-variant analysis. With suchgenesis, the tools may then be employed to verify raw Ultimate Analysislaboratory data. TABLE 5 Comparison of ′994 versus Present Invention R²(%) for Present Invention: R² (%) for ′994: MAF hydrogen + MAF hydrogen= MAF oxygen = Rank ƒ(MAF carbon) ƒ(MAF carbon) anthracite (an) 97.4099.80 semi-anthracite (sa) 90.34 98.60 High Volatile (hvAb, hvBb, 81.7799.77 hvCb, spot) sub-bituminous A (sub A) 90.52 99.50 Powder RiverBasin 71.93 99.77 sub-bituminous B (sub B) 86.64 99.43 sub-bituminous C(sub C) 87.36 98.13 Greek lignite 83.46 99.19 lignite A (lig A) 77.9396.97 Irish peat 65.90 98.45

The genetics of a fossil fuel of interest, if a viable concept, shouldallow specification of the chemical construct of its Rank. Indeed, itshould be consistent enough to be used to specify a coal's Ranks basedon Ultimate Analysis results. To produce such findings, note that Eqs.(61), (62) and (63) represent three equations and three unknowns: themolar ratios of carbon to molecular hydrogen, to molecular oxygen.Solving for these equations (using data from TABLE 2, TABLE 3 and TABLE4) results in specification of what a particular fossil fuel Rank trulymeans. TABLE 6 presents results for such analysis, presented by ageneric chemical makeup: CH_(c2)O_(c3) where the molar constants c2 andc3 are normalized to one mole of carbon. The consistency of TABLE 6 isapparent and belays the notion of separative analyses of TABLE 2, TABLE3 or TABLE 4 data. TABLE 6 employs ASTM D388 defined Ranks, which is notto be taken as limiting the application. For example, TABLE 6 indicatesthat the poorer lignites and Irish peat fuels, at the MAF level, aremore “friendly” toward the environment that the higher energy coals (an& sa) in that less effluent CO₂ is produced per burnt carbon. This wouldsuggest more research towards reducing lignite's mineral matter (Irishpeat has little mineral matter), and reducing the water content in thesetraditionally poor fuels. Using the type of data contained in TABLE 2,TABLE 3 and TABLE 4 to develop chemical makeups also will define theoccasional strange fuel. One such fuel is Bear Canyon coal, althoughmined in the Powder River Basin it is not a PRB coal (its data is notpart of FIG. 3 or FIG. 4). Bear Canyon computes asCH_(0.9197)O_(0.0762). The oxygen content of this coal indicates a sub Acoal while its hydrogen content indicates a lignite A or B. Since BearCanyon coal has little water content (most unlike PRB coals), itsgenetics, as taught herein, would suggest it being most environmentallyfriendly, it being closer to methane than any other known coal. TABLE 6Reduction of Multi-Variant Analysis to CH_(c2)O_(c3) Hydrogen OxygenPractical Rank (c2) (c3) Oxygen Range graphite 0.0000 0.0000 notapplicable anthracite (an) 0.2600 0.0191 ≧0.009, ≦0.024 semi-anthracite(sa) 0.4803 0.0283 ≧0.025, ≦0.054 High Seas (hvAb, hvBb, spot) 0.78440.0790 ≧0.055, ≦0.121 sub-bituminous A (sub A) 0.7661 0.1640 ≧0.122,≦0.170 Powder River Basin 0.8136 0.1751 ≧0.171, ≦0.183 sub-bituminous B(sub B) 0.8348 0.1900 ≧0.184, ≦0.200 sub-bituminous C (sub C) 0.88080.2074 ≧0.201, ≦0.215 lignite A (lig A) 0.8295 0.2221 ≧0.216, ≦0.230Greek lignite (lig B) 1.0788 0.4249 ≧0.390, ≦0.458 Irish peat 1.13140.4888 ≧0.459, ≦0.520 methane 4.0000 0.0000 not applicable

The consistency of TABLE 6 suggests that these findings be used toover-check laboratory Ultimate Analyses. The LECO Corporation, St.Joseph, Mich. state in the U.S. manufacture laboratory equipment whichis used to determine Ultimate Analyses. Their equipment includes theLECO CHN 600 instrument for determining elemental carbon (C), hydrogen(H) and nitrogen (N). Their LECO CHN 132 instrument determines elementalsulfur (S). The PerkinElmer Inc., Wellesley, Md. state in the U.S.manufactures a Model 2400 Series II CHNS/O Analyzer for elementalcarbon, hydrogen, nitrogen, sulfur and oxygen (by difference). Theseinstruments would benefit when analyzing coal samples by incorporatingthe teachings associated with TABLE 6. Many such analyzers run in anautomatic fashion, analyzing a number of samples at the same time andthus convenient to form multi-variant relationships resulting in similardata to that found in TABLE 2, TABLE 3 and TABLE 4. A data processingdevice would then reduce such data to a CH_(c2)O_(c3) form or itsequivalence. The ability of the laboratory to report data outliersassociated with such analyses would greatly improve diagnostics whentesting coal samples; and would assist in discovery of unique fuels(such as Bear Canyon coal). Specifically, this invention consists of adata processing device for evaluating Ultimate Analysis data, the devicecomprising: a) a data acquisition device to collect data from thethermal system including at least a selection of Choice OperatingParameters, the data acquisition device producing a set of acquiredsystem data; b) a computer with a processing means; c) a set ofinstructions for configuring the processing means to determine a fuelchemistry of the fossil fuel and to receive as input the set of acquiredsystem data, resulting in a programmed computer; d) means by which theprogrammed computer receives as input the set of acquired system data;e) the programmed computer producing the fuel chemistry of the fossilfuel; and f) means for reporting the fuel chemistry of the fossil fuelto assist in the operation of the thermal system. Further, the inventionalso comprises a means to compare an Ultimate Analysis with a set ofdescriptive fossil fuel data based on the genetics of fossil fuelsorganized by categories (such as TABLE 6) including instructions toidentify outlier Ultimate Analysis data. The following notes apply: 1)“a set of ultimate analysis instruments” means one or more than oneinstrument, examples of such instruments are cited above; 2) oxygen istypically computed by difference (i.e., 0 is produced by 1.0 minus C, H,N and S); 3) elemental concentrations are typically provided as weightfractions, conversion to molar is taught through Eqs. (94) & (93); 4) “adata processing” may be any one of the following: a device integratedwithin the ultimate analysis instrument, a common personal computer, aspecialized computer, a hand-held computer, or an integrated circuit;and 5) the “genetics of fossil fuels” is a defined concept (itsdescriptive material being taught throughout this disclosure, e.g., Eqs.(61), (62), (63), (72), FIG. 16, FIG. 18, TABLE 6, etc.) and includesall numerical results herein. Also note that a comparison of coal Ranksassumes a nominal range of uncertainty about oxygen values found inTABLE 6, said uncertainties being found after analyses and are indicatedin TABLE 6. Comparison of coal Ranks may also assume ranges ofuncertainty about hydrogen (i.e., the “c2” term).

The consistency of multi-variant analyses leading to the genetics offossil fuels, has proven definitive for a wide variety of fuels, butalso has proven indicative of poor industrial practices when obtainingUltimate Analyses. As demonstrated, multi-variant analysis is definitivefor the following coals, lignites and peat: an, sa, sub A, Powder RiverBasin, sub B, sub C, lig A, Greek lignite (lig B), and Irish peat.However, such findings as these have not been found universal. Theresearch supporting this invention has found that the volatile Ranks ofcoal (lvb, mvb, hvAb, hvBb and hvCb) do not produce high R² values whenusing analyses produced by laboratories following ASTM procedures. Thereason for this is aggressive heating of laboratory samples performedbefore Ultimate Analyses which drives off hydrogen-base materials whichare not tested. Although the R² values for such fuels are considerablyhigher when using multi-variant analysis, results are not satisfyinggiven the high accuracy results discovered for non-volatile fuels. ForMAF molar fuel carbon plus MAF molar fuel oxygen versus MAF molar fuelhydrogen R² values include: 88.35% for lvb; 91.44 for mvb; 84.51% forhvAb; 73.92% for hvBb; and 69.72% for hvCb. The database considered forFIG. 5, FIG. 6 and FIG. 7A, although internally consistent, was editedto eliminate what was believed to be the effects of volatilehydrocarbons driven off by aggressively heating laboratory samples, allfrom the U.S. The database considered for FIG. 5, FIG. 6 and FIG. 7Aobtained from non-U.S. laboratories was not edited. Other than advisingU.S. laboratories not to over-heat volatile coal samples, the inventivepoint is that multi-variant analysis affords an excellent method ofchecking that coal samples result in consistent Ultimate Analyses andcalorific values.

L₁₀ Factor

Taught in '994 via its Eq. (72) is use of a “fuel factor”. Taught in'877, U.S. Pat. No. 6,651,035, U.S. Pat. No. 6,745,152, applicationUS2004/128111 and application WO2003/091881 all via an Eq. (72A-alt), isuse of a “L Factor” for correction of effluent errors and for use in thedetection of tube failures in steam generators. Both the “fuel factor”of '994, and the “L Factor” of '877, etc. are the same quantity, hereindefined as the L₅ Factor. Taught in U.S. Pat. No. 6,560,563 is the useof an “L Factor”. Taught in U.S. Pat. No. 6,691,054 is the use an “FFactor”. Prior to the development of the present invention, the L₅Factor was found adequate as a descriptive quantity which, when plottedas a function of MAF molar fuel diatomic oxygen, could be normalized insuch a manner as to produce a constant value. A corrected and constantL₅ Factor (L_(5-corr)) proved useful when incorporated with a number ofinventions associated with The Input/Loss Method. However, when usedwith Irish peat, Powder River Basin coals and High Seas coals, the L₅Factor showed poor correlation. Thus in parallel with the development ofthe genetics of fossil fuels, and guided by that development, a new LFactor was discovered, termed the L₁₀ Factor, which indicates a highdegree of predictability for a wide range of fuels, including Irishpeat, Powder River Basin coals and High Seas coal. Its corrected value,L_(10-corr), is essentially constant. The L₁₀ Factor is defined by thefollowing, common units of measure being (mass of dry effluent)/(mass ofMAF fuel):L ₁₀ ≡[x _(DRY-theor) N _(DRY-Fuel) +a _(DRY-theor)(1.0+φ_(Ref))N _(Air)−J _(theor) N _(H2O) −x _(DRY-theor)α_(DRY-10) N _(Ash)]/(x _(MAF-theor)N _(MAF-Fuel))  (70)This form is taken to accent combustion moisture and ash terms (versus adirect effluent calculation). Note that Eq. (70)'s nomenclature followsEq. (29F), but where a dried fuel is burned theoretically, producing noeffluent O₂, nor pollutants; and divided by the mass ofmoisture-ash-free fuel per the stoichiometric base. Note thatx_(DRY-theor) is the moles of dried fuel based on theoreticalcombustion; N_(DRY-Fuel) is the molecular weight of dried fuel;a_(DRY-theor) is the moles of ambient dry air required to theoreticallycombust the dried fuel; etc.

When L₁₀ is plotted against either MAF molar fuel diatomic oxygen or thesum of MAF molar fuel carbon plus MAF molar fuel diatomic hydrogen, ahigh degree of predictability is found. FIG. 15, plotting High Seas coaldata indicates an R² value of 97.27%. Using the same data as for FIG.15, FIG. 16 plots against MAF molar fuel carbon plus MAF molar fueldiatomic hydrogen, indicating an R² value of 99.25%. FIG. 17 plots lowenergy fuels against MAF molar fuel oxygen. Using the same data as forFIG. 17, FIG. 18 plots against MAF molar fuel carbon plus MAF molar fueldiatomic hydrogen. The resultant correlations may be represented by thefollowing:L ₁₀ =G _(OHC1) +H _(OHC1)α_(MAF-3)  (71)L ₁₀ =G _(OHC2) +H _(OHC2)(α_(MAF-4)+α_(MAF-5))  (72)

The regression constants, G_(OHCk) and H_(OHCk), for a number of Ranks,are presented in TABLE 7 and TABLE 8. Note that FIG. 16 also indicatesthe results of correcting L₁₀ such that a constant (corrected) value maybe used with '877 methods. In the Preferred Embodiment, L₁₀ is correctedusing the following formulation:L _(10-corr) ≡L ₁₀ +[−H_(OHC2)(α_(MAF-4)−α_(MAF-4-Ref)+α_(MAF-5)−α_(MAF-5-Ref))]  (73)

where the reference values of the fuel (α_(MAF-4)-Ref and α_(MAF-5-Ref))are arbitrarily chosen, but should generally reflect the actual fuel andits reference MAF calorific value. FIG. 16 indicates essentially astraight line representation of the corrected L_(10-corr). Notably theL₁₀ Factor indicates no correlation when plotted against MAF molar fuelcarbon plus MAF molar fuel diatomic oxygen, nor against MAF molar fueldiatomic hydrogen plus MAF molar fuel diatomic oxygen. TABLE 7 L10 vs.MAF Molar Diatomic Oxygen Rank G_(OHC1) H_(OHC1) R² (%) anthracite (an)12.554270 −39.570934 93.12 semi-anthracite (sa) 12.721190 −43.26172894.71 High Seas (hvAb, hvBb, spot) 12.864510 −45.922948 97.27sub-bituminous A (sub A) 12.565156 −40.587183 98.72 Powder River Basin12.772919 −43.423015 99.61 sub-bituminous B (sub B) 12.601279 −41.26631498.82 sub-bituminous C (sub C) 12.434765 −39.130897 97.58 Penn Bit.Waste (Glob) 12.520164 −40.942945 92.68 lignite A (lig A) 12.448910−39.311755 97.94 Greek lignite 11.922373 −35.957530 99.27 Irish peat11.763082 −33.769078 98.60

TABLE 8 L10 vs. MAF Molar Fuel Carbon + Diatomic Hydrogen Rank G_(OHC2)H_(OHC2) R² (%) anthracite (an) −24.934121 37.685859 94.58semi-anthracite (sa) −31.027299 44.067901 95.90 High Seas (hvAb, hvBb,spot) −33.818323 47.085129 99.25 sub-bituminous A (sub A) −30.12565443.155046 98.425 Powder River Basin −29.52912 42.485604 99.65sub-bituminous B (sub B) −27.727421 40.593960 98.57 sub-bituminous C(sub C) −28.664285 41.636430 95.03 Penn Bit. Waste (Glob) −35.32843348.873806 94.65 lignite A (lig A) −27.384762 40.214575 96.63 Greeklignite −22.184593 34.500349 99.21 Irish peat −22.438731 34.581539 97.18

Perhaps as expected from '877 teachings, L₁₀ is linear with MAF molarfuel diatomic oxygen, but also linearity is achieved with MAF molar fuelcarbon plus MAF molar fuel diatomic hydrogen (as lead by multi-variantanalysis). Thus Eqs. (71) and (72) may be equaled for a given group offuels, forming an independent equation to be used in the matrix solutionas based on the multi-variant relationship of Eq. (72):−ξ_(L1)α_(MAF-3)+α_(MAF-4)+α_(MAF-5)=ξ_(L2)  (74)where:ξ_(L1) ≡H _(OHC1) /H _(OHC2)  (75)ξ_(L2)≡(G_(OHC1) −G _(OHC2))/H _(OHC2)  (76)Determining Complete As-Fired Fuel Chemistry

The mathematical description of the thermal system used to obtain acomplete As-Fired fuel chemistry is principally described by Eqs. (30)through (34), (42), (54) and (58), all using the combustion equation Eq.(29F); details afforded in the above teachings are included. Inaddition, the mathematical description of the thermal system used toobtain a complete As-Fired fuel chemistry includes the teachings of thissection (six paragraphs). As taught above, the genetics of fossil fuelsbased on multi-variant analysis has justified two independent equationswhich add to the matrix solution. Returning to the stoichiometrics ofEqs. (30) through (34), the following add to the 3×3, 4×4 or 5×5 matrixsolution (explained below). If twice Eq. (32) is subtracted from Eq.(31), substituting for “x” via Eq. (33) results in an expressionapplicable for a 3×3 matrix solution:−2α_(MAF-3)−ξ_(C1)α_(MAF-4)+α_(MAF-5)+0.0=0.0  (77)where:ξ_(C1)≡(Γ_(H2O)−2Γ_(O2))/Γ_(CO2)  (78)For the sulfur term, combining Eq. (34) and (33) results in anexpression applicable for the 4×4 or 5×5 matrix solution:+0.0+Γ_(SO2)α_(MAF-4)+0.0−Γ_(CO2)α_(MAF-6)+0.0=0.0  (79)In addition, an expression applicable for the 5×5 matrix solution isdeveloped by substituting terms of Eq. (42) into Eq. (38) such that theterm x_(MAF)α_(MAF-6) is incorporated into the combined Eqs. (31) &(32); reducing terms yields:−2α_(MAF-3)−ξ_(S1)α_(MAF-4)+α_(MAF-5)+2α_(MAF-6)+0.0=0.0  (80)where:ξ_(S1)≡Γ_(H2O)−2Γ_(OHS)−2ξ_(S6))/Γ_(CO2)  (81)ξ_(S6) ≡k _(Act)[Γ_(SO3)/(1.0−Γ_(SO3))]/(2Γ_(ESP))+b_(PLS)[σ/2−1.0−γ+σz/2+σΓ_(SO3)/(2.0−2Γ_(SO3))]  (82)Also, the sum of all MAF molar constituents becomes applicable for the5×5 matrix solution as it allows solution for fuel nitrogen (α_(MAF-1)):α_(MAF-3)+α_(MAF-4)+α_(MAF-5)+α_(MAF-6)+α_(MAF-1)=1.0  (83)

It becomes obvious then that the following five equations having fiveunknowns (an Ultimate Analysis) may be resolved in conventional fashionusing a 5×5 matrix solution:

From genetics (based on L₁₀), Eq. (74):−ξ_(L1)α_(MAF-3)+α_(MAF-4)+α_(MAF-5)+0.0+00=ξ_(L2)From genetics, Eq. (64):+α_(MAF-3)/2−K _(OHC3)α_(MAF-4)+α_(MAF-5)/2+0.0+0.0=J _(OHC3)From stoichiometrics, Eq. (80):−2α_(MAF-3)−ξ_(S1)α_(MAF-4)+α_(MAF-5)+2α_(MAF-6)+0.0=0.0From stoichiometrics, Eq. (79):+0.0+Γ_(SO2)α_(MAF-4)+0.0−Γ_(CO2)α_(MAF-6)+0.0=0.0From stoichiometrics (MAF balance), Eq. (83):+α_(MAF-3)+α_(MAF-4)+α_(MAF-5)+α_(MAF-6)+α_(MAF-1)=1.0.

However, the above system of equations may be reduced given situationsunique to a given thermal system. If little fuel nitrogen is present (orit is highly predictable), then four equations having four unknowns (anUltimate Analysis less nitrogen) may be resolved in using a 4×4 matrixsolution, nitrogen being held constant or equated to (1.0−Σ_(j=1,3,4,5)α_(MAF-j)):

From genetics (based on L₁₀), Eq. (74):−ξ_(L1)α_(MAF-3)+α_(MAF-4)+α_(MAF-5)+0.0=ξ_(L2)From genetics, Eq. (64):+α_(MAF-3)/2−K _(OHC3)α_(MAF-4)+α_(MAF-5)/2+0.0=J _(OHC3)From stoichiometrics, Eq. (77):−2α_(MAF-3)−ξ_(C1)α_(MAF-4)+α_(MAF-5)+0.0=0.0From stoichiometrics, Eq. (79):+0.0+Γ_(SO2)α_(MAF-4)+0.0−Γ_(CO2)α_(MAF-6)=0.0.

Further, if both fuel nitrogen and fuel sulfur are either highlypredictable (and/or the fuel contains no sulfur), then three equationshaving three unknowns comprising the base Oxy-Hydrocarbon model as anintrinsic out-come of the genetics of fossil fuels, may then be resolvedusing a 3×3 matrix solution. Specifically, sulfur may be held constant,including zero, or resolved via Eq. (34) after determining a 4 from the3×3 matrix solution.

From genetics (based on L₁₀), Eq. (74):−ξ_(L1)α_(MAF-3)+α_(MAF-4)+α_(MAF-5)=ξ_(L2)From genetics, Eq. (64):+α_(MAF-3)/2−K _(OHC3)α_(MAF-4)+α_(MAF-5)/2=J _(OHC3)From stoichiometrics, Eq. (77):−2α_(MAF-3)−ξ_(C1)α_(MAF-4)+α_(MAF-5)=0.0.Such collections of equations for the aforementioned matrix solutionsare certainly not unique, to one skilled several variations will becomeapparent given any study. For example the above 3×3 matrix solutionobviously may invoke Eq. (83) such that its right-hand side is constant;i.e., known and constant nitrogen (α_(MAF-1)) and sulfur (α_(MAF-6)):From genetics, Eq. (64):+α_(MAF-3) −K _(OHC3)α_(MAF-4)+α_(MAF-5) =J _(OHC3)From stoichiometrics, Eq. (77):−2α_(MAF-3)−ξ_(C1)α_(MAF-4)+α_(MAF-5)=0.0From stoichiometrics (MAF balance), Eq. (83):+α_(MAF-3)+α_(MAF-4)+α_(MAF-5)=(1.0−α_(MAF-1)−α_(MAF-6))As another example, the 4×4 matrix solution may also employ the MAFbalance of Eq. (83), replacing the L₁₀ relationship, by settingα_(MAF-1) constant; the right-hand side of Eq. (83) becoming(1,0-α_(MAF-1)) after re-arranging. Although the 5×5 matrix solution,involving all MAF fuel constituents, is the Preferred Embodiment, theERR-CALC and HEATRATE programs are provided with an input option whichselects which of these matrix solutions is to be employed. Suchselection is based principally on the predictability of the nitrogen andsulfur fuel components (e.g., knowing whether the fuel has sulfur); ofcourse when employing the 5×5 matrix solution, such judgement is notrequired. In summary, the operator of the thermal system or a vendorselling to said operator may be using the genetics of the fossil fuelbased on multi-variant analysis as taught herein, and may be using amathematical description of the thermal system as taught herein toimprove the system. On the other hand, the operator of the thermalsystem or a vendor selling to said operator may be developing thegenetics of the fossil fuel based on multi-variant analysis as taughtherein and may be developing a mathematical description of the thermalsystem based on the teachings herein to improve the system.

Once the Ultimate Analysis of MAF fuel constituents is resolved, MAFfuel moles may be computed from Eq. (56): x_(MAF)=Γ_(CO2)/α_(MAF-4).With the Ultimate Analysis of MAF fuel constituents known, with MAF fuelwater of Eq. (42) and, with x_(MAF), AF_(Act) and “a”, MAF fuel ash ofEq. (54) may then be resolved in an explicit manner. To summarize, thematrix solutions presented in the preceding four paragraphs employresults from the genetics of the fossil fuel, based on multi-variantanalysis, and employ mathematical description of the thermal systembased on stoichiometrics. Terms are not mixed. The features incorporatedinto the matrix solutions presented in the preceding threeparagraphs—representing a considerable inventive step beyond '994include:

-   -   the use of multi-variant analysis resulting in applying at least        one of the relationships described by Eqs. (61), (62), (63),        and (71) combined with (72);    -   the genetics for all important Ranks of coal is listed in TABLES        2, 3, 4, 7 and 8, eliminates the need for routine historical        data;    -   R² values typically exceed 98%, allowing the genetics of the        fossil fuel of interest to be used to interrogate laboratory        results;    -   the mathematical description does not intermingle correlation        constants (resultant from multi-variant analysis) with        stoichiometric terms, i.e., Eqs. (77) and (83) contain only        stoichiometric terms;    -   fuel nitrogen need not be kept constant (when using the 5×5        matrix solution);    -   the need for minimum and maximum limits applied to fuel        concentrations is obviously eliminated since the computed MAF        constituents must satisfy all equations in the matrix solution,        numerical consistency is intrinsic.

Thus all fuel constituents, and the fuel moles, are therefore determinedon a MAF basis. From these values, the wet base molar fuel fractions arethen determined, as are the wet base moles of fuel (x) and the wet base(As-Fired) weight fractions (WF_(j)) of all fuel constituents j:α_(j)=α_(MAF-j)/(1.0+α_(MAF-2)+α_(MAF-10))  (90)x=x _(MAF)(1.0+α_(MAF-2)+α_(MAF-10))  (91)xα _(j)≡x_(MAF)α_(MAF-j)  (92)WF _(j)=α_(j) N _(j)/(Σα_(j) N _(j))  (93)WF _(DRY-j) =WF _(j)/(1.0−WF ₂)  (94)Determining Calorific Value, Boiler Efficiency, Fuel and Effluent Flows

This section includes the mathematical description of the thermal systemused to obtain a calorific value, boiler efficiency, fuel and effluentflows. Having obtained a complete As-Fired fuel chemistry, the fuel'scalorific value (i.e., heating value) is next computed. Following theteachings of '994, calorific value is determined based on a differentialanalysis. References are cited in '994. Note that the term N_(MAF) isthe molecular weight of the MAF-base fuel (without fuel water andwithout fuel ash).

For calorific value units of measure in kJ/kg:ΔHHV _(MAF-delta) =HHV_(MAF-Ref)−(−414928.58α_(MAF-3)+427034.81α_(MAF-4)+181762.20α_(MAF-5)+297011.59α_(MAF-6))_(Ref)/N _(MAF-Ref)  (98A)HHV_(MAF-uncorr)=(−414928.58α_(MAF-3)+427034.81α_(MAF-4)+181762.20α_(MAF-5)+297011.59α_(MAF-6))_(Actual)/N _(MAF-Actual)  (99A)For calorific value units of measure in Btu/lbm:ΔHHV _(MAF-delta) =HHV_(MAF-Ref)−(−178387.18α_(MAF-3)+183591.92α_(MAF-4)+78143.68α_(MAF-5)+127692.00α_(MAF-6))_(Ref)/N _(MAF-Ref)  (98B)HHV_(MAF-uncorr)=(−178387.18α_(MAF-3)+183591.92α_(MAF-4)+78143.68α_(MAF-5)+127692.00α_(MAF-6))_(Actual)/N _(MAF-Actual)  (99B)HHV _(MAF) ═HHV _(MAF-uncorr) +ΔHHV _(MAF-delta)  (100)HHV _(DRY) ═HHV _(MAF)(1.0−WF _(DRY-10))  (101)HHV _(AF) ═HHV _(DRY)(1.0−WF ₂)  (102)

The preferred correlations used to determine calorific values for thepresent invention are based on chemical binding energies. Studies havedemonstrated that traditional correlations, such as the Mott-Spoonercorrelation based on Dulong's formula—well known in the industry—are notadequate. The Preferred Embodiment of the present invention requires atleast the coefficients used in determining calorific value to fallwithin certain ranges associated with three principal constituents ofcoal. Studies have indicated that using the above preferred constants,which fall within the required ranges, reduces the standard deviation offive dozen wildly varying coal analyses from ±530 to ±214 ΔkJ/kg (±228to ±92 ΔBtu/lbm, i.e., ΔBtu/pound). The ranges of these coefficients,i.e., multiples the molar fractions α_(j) in Eqs. (98A) and (99A), forunits of kJ/kg, or their equivalent weight fractions (for thispresentation of ranges, the symbol WF_(j) represents percent weight ofj), include the following: for carbon molar fraction 390358α_(carbon/N)_(fuel) to 429994α_(carbon)/N_(fuel), or in weight percent carbon,325WF_(carbon) to 358WF_(carbon); for hydrogen molar fraction180623α_(hydrogen)/N_(fuel) to 293109α_(hydrogen)N_(fuel) assuming thediatomic hydrogen, or in weight percent hydrogen, 896WF_(hydrogen) to1454WF_(hydrogren); and for also for oxygen molar fraction−275190α_(oxygen)/N_(fuel) to −579178α_(oxygen)/N_(fuel) assumingdiatomic oxygen, or in weight percent oxygen, −86WF_(oxygen) to−181WF_(oxygen). These ranges are independent of the fuel base, whetherMAF, dry or As-Fired fuel constituents are used. Also, the ranges ofthese coefficients, i.e., multiples the molar fractions α_(j) in Eqs.(98B) and (99B), for units of Btu/lbm, or their equivalent weightfractions (for this presentation of ranges, the symbol WF_(j) representspercent weight of j), include the following: for carbon molar fraction168154α_(carbon)/N_(fuel) to 184969α_(carbon)/N_(fuel), or in weightpercent carbon, 140WF_(carbon) to 154WF_(carbon); for hydrogen molarfraction 77611α_(hydrogen)/N_(fuel) to 125993α_(hydrogen)/N_(fuel),assuming diatomic hydrogen, or in weight percent hydrogen,385WF_(hydrogen) to 625 WF_(hydrogen); and for the oxygen molar fraction−118396α_(oxygen)/N_(fuel) to —249591α_(oxygen)/N_(fuel) assumingdiatomic oxygen, or in the weight percent oxygen, −37WF_(oxygen) to−78WF_(oxygen). These ranges are independent of the fuel base, whetherMAF, dry or As-Fired fuel constituents are used.

Boiler efficiency is defined as either gross calorific based, η_(B-HHV)(i.e., higher heating value, HHV), or net calorific based, 71B-LHV(i.e., lower heating value, LHV). In the Preferred Embodiment boilerefficiency is determined using the methods of '429. Another of theInput/Loss methods may be used to determine boiler efficiency, providedconsistency between boiler efficiency, fuel flow and effluent flow ismaintained. The details of such consistency is thoroughly discussed in'994. In addition to '429, the following procedures for determiningboiler efficiency have sufficient accuracy and consistency for use bythis invention: the American Society of Mechanical Engineers' (ASME)Performance Test Codes (PTC) 4.1 and 4; the German standard “AcceptanceTesting of Steam Generators, DIN 1942, DIN DEUTSCHES Institut FurNormung E.V., February 1994; the European standard (draft) prEN12952-15:1999 (also: CEN/TC 269/WG 3 N 337), “Water-Tube Boilers andAuxiliary Installations—Part 15: Acceptance Tests”, November 1999,European Committee for Standardization, Central Secretariat, rue deStassart, 36, Brussels; and the British Standard “Code for AcceptanceTests on Stationary Steam Generators of the Power Station Type”, BS2885:1974, ISBN: 0 580 08136 2.

As taught in '429, and considered important for this invention, is thatthe As-Fired fuel flow compute identically from either efficiency base:$\begin{matrix}{m_{AF} = {\frac{BBTC}{\eta_{B\text{-}{HHV}}\left( {{HHVP} + {HBC}} \right)} = \frac{BBTC}{\eta_{B\text{-}{LHV}}\left( {{LHVP} + {HBC}} \right)}}} & (103)\end{matrix}$For Eq. (103), such computations, if following the Preferred Embodiment,required that: 1) the Firing Correction term HBC be employed; 2) thecalorific values be properly corrected, if needed, for a constantpressure process (resulting in HHVP or LHVP); and 3) the calorimetrictemperature, T_(Cal), be consistently employed in all terms making upboiler efficiency. All of these teachings may be found in '429. However,this invention is not limited to the use Eq. (103) and the HBC term(although preferred), as many of the industrial standards to set HBC tozero and use methods other than '429 to compute boiler efficiency; theimportant criteria is to maintain consistency of use when determiningfuel flow, effluent flow, etc. based on boiler efficiency, BBTC andcalorific value.

Knowing the complete As-Fired fuel chemistry leads to a high accuracyboiler efficiency, a boiler efficiency which in-turn leads to systemefficiency. The systems' over-all thermal efficiency is defined in aconsistent manner, as taught in '994. System thermal efficiency is alsoexpressed in-terms of heat rate, HR (kJ/kWh or Btu/wKh, i.e.Btu/kilowatt-hour), the reciprocal of efficiency with units conversion.$\begin{matrix}{\eta_{{SYS}\text{-}{HHV}} = {W_{output}/\left\lbrack {m_{AF}\left( {{HHVP} + {HBC}} \right)} \right\rbrack}} & \left( {104A} \right) \\{\quad{= {W_{output}{\eta_{B\text{-}{HHV}}/{BBTC}}}}} & \left( {104B} \right) \\{\eta_{{SYS}\text{-}{LHV}} = {W_{output}/\left\lbrack {m_{AF}\left( {{LHVP} + {HBC}} \right)} \right\rbrack}} & \left( {105A} \right) \\{\quad{= {W_{output}{\eta_{B\text{-}{LHV}}/{BBTC}}}}} & \left( {105B} \right)\end{matrix}$For heat rate units of kJ/kWh:HR _(HHV)=3600.0000/η_(SYS-HHV)  (106A)HR _(LHV)=3600.0000/η_(SYS-LHV)  (106B)For heat rate units of Btu/kWh:HR _(HHV)=3412.1416/η_(SYS-HHV)  (107A)HR _(LHV)=3412.1416/η_(SYS-LHV)  (107B)

By knowing the complete As-Fired fuel chemistry and the As-Fired fuelflow, and using a mathematical description of the thermal system basedon stoichiometrics, individual effluent flows, m_(species-i) (kg/hr orlb/hr), may then be determined:m _(species-i) =m _(AF)Φ_(i) N _(i)/(xN _(AF))  (108)where Φ_(i) is the moles of an effluent species on a dry-basis; i.e.,Φ_(i) is the effluent concentration in moles. The term Φ_(i) derivesdirectly from solutions or measurements of the right-hand terms of Eq.(29F), for example Φ_(SO2)=k_(Act). To determine the total effluentflow, Eq. (108) may be summed, noting that ΣΦ_(i)=100.0 moles.Individual emission rates, termed ER_(i), in units of measure followingthose of reciprocal calorific value (kg-effluent/million-kJ, orpounds-effluent/million-Btu of fuel energy input), is given by thefollowing: $\begin{matrix}{{ER}_{i} = {10^{6}{m_{{species} - i}/\left( {m_{AF}{HHV}_{AF}} \right)}}} & \left( {109\quad A} \right) \\{\quad{= {10^{6}\Phi_{i}{N_{i}/\left( {{xN}_{AF}{HHV}_{AF}} \right)}}}} & \left( {109\quad B} \right)\end{matrix}$As seen, an individual emission rate may be evaluated independently ofthe As-Fired fuel flow, Eq. (109B). However, the computational accuracyof the fuel flow, as determined using the present approach,intrinsically affects an individual emission rate through HHV_(AF), xand N_(AF). Further, the process described herein allows thedetermination of total effluent dry volumetric flow, at standardconditions of gaseous effluent, denoted by VF, as required byenvironmental regulations. VF is determined by the following (instandard-m³/sec or standard-ft³/hr):VF=ρ _(gas) m _(AF) N _(gas)/(xN _(AF))  (110)where ρ_(gas) and N_(gas) are the standard density and average molecularweight of the effluent dry gas.Correction of Choice Operating Parameters and System Benchmarking

This section includes the mathematical description of the thermal systemused to obtain a multidimensional minimization analysis. This inventionrecognizes that those products from combustion which are used todetermine a complete As-Fired fuel chemistry, as measured by routinepower plant instrumentation, may have error associated with theirsignals. As taught herein, quantities employed to determine fuelchemistry consist not only of the principle effluents CO₂, H₂O and O₂but also the Air Pre-Heater Leakage Factor, etc. This invention hasdefined Choice Operating Parameters (COP) as all parameters which maydirectly impact system stoichiometrics, and thus may impact thedetermination of fuel chemistry. To correct errors in COPs one of twomethods may be employed: 1) apply judgement based on a power engineer'sexperience with a particular instrument (e.g., plot signals vs. time,compare multiple signals reading the same value, etc.); and 2) use themethods as taught in '877. For the Preferred Embodiment, '877 methodsare herein modified as follows. First, the use of the L Factor as aSystem Effect Parameter (SEP) must not employ L₅, but L₁₀ as defined viaEq. (70). Second, '877 methods must recognize that the relative humidityassociated with the combustion air represents a significant sensitivityto system stoichiometrics when employing the methods of this invention.Third, a modified Objective Function has shown to be better suited thegenetics of fossil fuels. In the Preferred Embodiment, COPs may beselected by the power plant engineer from any combination or all of thefollowing:Λ_(1S)=d_(Act); Stack CO₂ (with effects from Air Pre-Heaterleakage)  (111S)Λ_(1B) =d _(Act) R _(Act); Boiler CO₂ (without effects from AirPre-Heater leakage)  (111B)Λ_(2S) =J _(Act) ≡j+b _(A)β; Stack H₂O (with H₂O from Air Pre-Heaterleakage)  (112S)Λ_(2B) =jR _(Act); Boiler H₂O (without H₂O from Air Pre-Heaterleakage)  (112B)Λ₃=AF; Air/Fuel ratio (for explicit determination of fuel ash)  (113)Λ₄=R_(Act); Air Pre-Heater Leakage Factor  (114)Λ₅=A_(Act); Concentration of O₂ in the combustion air  (115)Λ₆=m_(LS); System's indicated plant limestone flow  (116)Λ_(7S) =G _(Act) ≡g+aβ; Stack O ₂ (with Air Pre-Heater leakage)  (117S)Λ_(7B) =gR _(Act); Boiler O₂ (without Air Pre-Heater leakage)  (117B)Λ₈=m_(T); Tube leakage flow rate  (118)Λ₉=H_(Act); Relative humidity of ambient air local to the thermalsystem  (119)

Selecting one or more of the Choice Operating Parameters for use mustdepend on common understanding of power plant stoichiometrics andassociated relationships to physical equipment. What the ERR-CALCprogram produces (FIG. 20B, item 255), employing one or more of theminimization techniques as taught by '877, are correction factors, foreach chosen Λ_(k) which are then applied to the raw uncorrected signal(Λ_(0-k)). The resulting corrected signal is then processed within theFuel Iterations, defined in conjunction with a description of FIG. 20. Amultidimensional minimization analysis includes driving an ObjectiveFunction, F({right arrow over (x)}), to a minimum value (ideally zero),by optimizing COPs. Although COPs (Λ_(k)) values do not appear in theObjective Function, they directly impact SEPs directly. SEPs are driventowards Reference System Effect Parameters by the following:λ_(L)≡[(L ₁₀ −L _(10-Ref))/L _(10-Ref)]^(M) ^(L)   (120A)λ_(W)≡[(m _(AF) −m _(AF-PLT))/m _(AF-PLT)]^(M) ^(W)   (120B)λ_(H)≡[(HHV _(AF) −HHV _(AF-Ref))/HHV _(AF-Ref)]^(M) ^(H)   (120C)

In these equations The Objective Function most useful for the methodsand apparatus of this invention is given by Eq. (121). Note that theBessel function of the first kind of order zero (J₀) is highly suited tothe sensitivities found in coal-fired stoichiometrics.F({right arrow over (x)})=Σ _(kεK) {S _(i[)1.0−J ₀(λ_(L))]^(MC) ^(k) +S_(i[)1.0−J ₀(λ_(W))]^(MC) ^(k) +S _(i[)1.0−J ₀(λ_(H))]^(MC) ^(k)}  (121)In Eq. (121), the symbol MC_(k) is termed a Dilution Factor (asintroduced in '877), but here assigned individually by COP allowinggreater stability in solution. In Eq. (121) S_(k) is a scaling factorsaccounting for differing magnitudes of λ_(j). In Eq. (121), the symbolΣ_(kεK) indicates a summation on the index k, where k variables arecontained in the set K defined as the elements of {right arrow over(Λ)}. For example, assume the user has chosen the following: Λ_(1S) isto be optimized to minimize the error in L₁₀ and HHV_(AF), Λ_(2S) isoptimized for L₁₀ and m_(AF) (M_(W)=1.40), Λ₄ is optimized for L₁₀, andΛ_(7B) is optimized for L₁₀. Therefore: {right arrow over (Λ)}=(Λ_(1S),Λ_(2S), Λ₄, Λ_(7B)), K={Λ_(1S), Λ_(2S), Λ₄, Λ_(7B)}, thus {right arrowover (x)}=(x₁, x₂, x₃, x₄); x₁=S₁Λ_(1S); x₂=S₂Λ_(2S); x₃=S₃Λ₄;x₄=S₄Λ_(7B); where Eq. (121) for this example then becomes:F({right arrow over (x)})=S _(1{)[1.0−J ₀(λ_(L))]^(MC) ¹ +[1.0−J₀(λ_(H))]^(MC) ¹ }+S ₂{[1.0−J ₀(λ_(L))^(MC) ² ]+[1.0−J ₀(λ_(W))]^(MC) ² }+S _(3[)1.0−J ₀(λ_(L))]^(MC) ³ +S _(4[)1.0−J ₀(λ_(L))]^(MC) ⁴Upon optimization, COP correction factors (C_(k)) are determined simplyas: C_(k)=Λ_(k)/Λ_(0-k). Note that the only output from ERR-CALC arecorrection factors.

The consistency demonstrated herein by the genetics of the fossil fuels,as implemented by this invention for the determination of fuelchemistry, has proven of such remarkable consistency and accuracy that,it is believed, ambient relative humidity may offer a vehicle throughwhich a power plant's monitoring system may be benchmarked. Thisstatement is saying that a system's stoichiometrics (i.e., fuelchemistry versus effluent production of CO₂, H₂O, O₂, etc., determinedby The Input/Loss Method) may be verified using an independent parameterassociated with combustion, ambient relative humidity, which is notdirectly influenced by the understanding (or not) of fuel chemistry,fuel flow and boiler efficiency. However, a relative humidity computedby The Input/Loss Method is indeed greatly affected by fuel chemistry,an understood system stoichiometrics and calorific value; suchsensitivity on the computed is extreme. As a practical application, useof this benchmarking technique would verify reported carbon emissionsbased on the monitoring system's ability to replicate an environmentalparameter which would be measured by all parties, both regulator and thesystem operator. Of course other air psychrometric parameters such asspecific humidity, web bulb temperature, etc. might be used, butrelative humidity as ranging from 0.0 to 100% is most convenient for'877 optimization procedures.

The procedure for benchmarking an on-line monitoring system is thus: 1)monitor the power plant such that SEP for the plant's indicated plantfuel flow is invoked, optimizing on both the COP for effluent H₂O(Λ_(2S)), and the COP for relative humidity (Λ₉); 2) set to a constantthe input of relative humidity to The Input/Loss Method; 3) ERR-CALC,using '877 methods modified as above, will produce correction factorsfor both Λ_(2S) and Λ₉; 4) bias the plant's indicated plant fuel flowuntil the corrected relative humidity computed by The Input/Loss Methodagrees with a directly measured (and independent) value. When agreementis reached, fuel chemistry, fuel calorific value (CV, dependent on fuelchemistry), boiler efficiency (dependent on fuel chemistry and CV) andthe energy flow to the working fluid heated by combustion products(BBTC) all must be accurate. Given this, all emission flows, e.g.,carbon emission, must be accurately computed; it may be nothing else. Asan example of such benchmarking FIG. 21 is a plot of an emulation of apower plant and its data in which the system's measured relativehumidity is being matched by a computed relative humidity. FIG. 21demonstrates stoichiometric understanding. Plotted are comparisonsbetween the indicated plant fuel flow and the computed. Note that upsetmarks on the computed fuel flow trace represent interruptions in whichfuel flow bias was being adjusted. An emulation of an actual system wasemployed for FIG. 21 since certain patent offices do not allowdemonstration of invention before filing. The indicated plant fuel flowwas shown to have an average bias of 2.41%.

Calculational Engine Apparatus for Input/Loss Methods

Obtaining a complete As-Fired fuel chemistry, including fuel water andfuel ash (as based on: a) using a genetics of the fossil fuel based onmulti-variant analysis; b) using a mathematical description of thethermal system; c) measuring a set of measurable Operating Parameters,including at least effluent concentrations of O₂ and CO₂, thesemeasurements being made at a location downstream of the heatexchanger/combustion region of the thermal system; d) obtaining aneffluent concentration of H₂O, as an obtained effluent H₂O; e) obtaininga fuel ash concentration selected from the group consisting of: aconstant value of fuel ash, a predictable value of fuel ash, a measuredvalue of fuel ash determined from a fuel ash instrument and a value offuel ash determined from explicit solution, as an obtained fuel ashconcentration; f) obtaining a concentration of O₂ in the combustion airlocal to the system; and g) obtaining the Air Pre-Heater LeakageFactor), may be incorporated into a fuel chemistry determining apparatusto improve the understanding of fossil-fueled thermal systems, includinga produced output provided from associated analytical models dependenton fuel chemistry. The produced output from the apparatus includes thefuel's calorific value (CV, dependent on fuel chemistry), boilerefficiency (dependent of fuel chemistry and CV), fuel flow per Eq.(103), and system efficiency of Eqs. (104) & (105). The produced outputfrom the apparatus thereby provides a means to assist the operator ofthe thermal system in the monitoring and improvement of systemefficiency on a continuous operating basis such as would be used for theon-line monitoring of power plants.

In summary, this invention includes an apparatus for assisting theoperation of a thermal system burning a fossil fuel, the apparatuscomprising: a) a data acquisition device to collect data from thethermal system including at least a selection of Choice OperatingParameters, the data acquisition device producing a set of systemacquired data; b) a computer with a processing means; c) a set ofinstructions for configuring the processing means to determine a fuelchemistry of the fossil fuel and to receive as input the set of systemacquired data, resulting in a programmed computer; d) means by which theprogrammed computer receives as input the set of system acquired data;e) the programmed computer producing the fuel chemistry of the fossilfuel; and f) means for reporting the fuel chemistry of the fossil fuelto an operator of the thermal system. The aforementioned computer may bea common personal computer, or, broadly, any data processing unit. Inaddition, set of instructions for configuring the processing means todetermine a fuel chemistry of the fossil fuel includes programming theteachings of this invention including the genetics of the fossil fuel,the mathematical description of the thermal system, determination of anUltimate Analysis of the fossil fuel, and determination of a completeAs-Fired fuel chemistry.

CONCLUSION

Although the present invention has been described in considerable detailwith regard to certain Preferred Embodiments thereof, other embodimentswithin the scope and spirit of the present invention are possiblewithout departing from the general industrial applicability of theinvention. For example, the descriptions of this invention assume that asteam generator's working fluid is water, however the general proceduresof this invention may be applied to any type of working fluid providedthat the working fluid is definable at the boundary of the system.Examples of other working fluids are: mixtures of water and organicfluids, organic fluids, liquid metals and so forth. Further, the conceptof multi-variant analysis leading to the genetics of fossil fuels waspresented with two elements (combinations of carbon, hydrogen andoxygen), which is the Preferred Embodiment. However, this invention isnot to be limited by this concept. Multi-variant analysis leading to thegenetics of fossil fuels may well employ three elements in anycombination: carbon, hydrogen, oxygen and sulfur. For example, Eq. (61)might be replaced with:α_(MAF-4)+α_(MAF-5)+α_(MAF-6)=J′_(OHC1)+K′_(OHC1)α_(MAF-3); thus forminga (carbon+hydrogen+sulfur) fit versus oxygen. Indeed, success has beenhad with such employments. Accordingly, the general theme and scope ofthe appended claims should not be limited to the descriptions of thePreferred Embodiment disclosed herein.

Although a Preferred Embodiment of the present invention has beendemonstrated via THE DRAWINGS and described in considerable detail theforegoing DESCRIPTION OF THE PREFERRED EMBODIMENT, it will be understoodthat the invention is not limited to the embodiments disclosed, butthose methods are capable of numerous rearrangements, modifications andsubstitutions without departing from the scope and spirit of the presentinvention as set forth and defined by the claims herein.

THE DRAWINGS

The FIGS. 1 through 18, and FIG. 21 have been discussed in detail withinthe foregoing DESCRIPTION OF THE PREFERRED EMBODIMENT. Analyticalfindings of these FIGURES are presented in TABLES 2, 3, 4, 7 and 8.TABLE 6 presents generic chemical makeups of numerous fossil fuels, whennormalized to carbon in the form CH_(c2)O_(c3).

FIG. 19 is a schematic representation of a thermal system, particularlya steam generator system illustrating use of stoichiometricrelationships important in applying this invention. It should be studiedin conjunction with combustion equation, Eq. (29F). FIG. 19 depicts asteam generator denoted as 20. In this system 20, a fuel feed 22 andcombustion air 24 are all provided to the upstream side region 26 of theheat exchanger/combustion region 28. Note that this region 28 does notinclude the air pre-heater 36. In addition, in some types of steamgenerators 20 such as fluidized bed combustors, other materials may beinjected into region 26, such as a flow of limestone 31 to minimizeeffluent SO₂ by chemically binding sulfur as CaSO₄. Other sorbents maybe injected to control sulfur, to control other pollutants, and/or tocontrol the combustion process. The fuel feed 22 contains, in general,combustible fossil material, water and mineral matter (commonly calledash); 22 represents an As-Fired fuel given it is the fuel being burnedafter crossing the system boundary 44. Fuel ash is an unburnablecomponent that passes through the system with little physical change,but which is heated and cooled. In the heat exchanger/combustion region28, the steam generator's fuel 22 is burned with the combustion air 24to form hot products of combustion. Heat from the products of combustionis transferred to a working fluid that enters 134 heat exchangers 132that are depicted as integral with the heat exchanger/combustion region28. The heated working fluid 130 is used in a manner appropriate to aworking fluid to generate a useful output 33 (for example, in aconventional power plant such useful output, BBTC, may be supplied to aturbine-generator cycle for the production of electrical power,W_(output)). Heat exchangers 132 may consist of a series of heatexchangers. There may be working fluid leakage 29 into the products ofcombustion 28 and into region 35, not associated with water in the fuelfeed 22, or moisture in the combustion air 24. Working fluid leakage 29consists of known flows, or flows which may be otherwise reasonablyassumed or determined; and may result from, for example, soot blowingassociated with coal-fired systems, or working fluid used to atomize thefuel 22 before combustion, or used in pollutant control processeslocated at 35 or 42. The products of combustion leave the heatexchanger/combustion region 28 on its downstream region 34, the coolerproducts of combustion then commonly flow through ducts, region 35,which may contain fly ash removal equipment, passing then to an airpre-heater 36, where a further portion of the combustion gas energy istransferred to an incoming air stream 38, which air then becomes thecombustion air 24. The total air delivered to 20 is the incoming airflow 25. In many cases, an air leakage flow 40 enters the flow of theproducts of combustion as it passes through the air pre-heater 36. Thefurther cooled products of combustion leave the air pre-heater 36 andpass to the Stack 42, the gases then being exhausted to the localenvironment 43. Within the steam generator system 20 the combustion gaspath is defined as that region encompassing the flow of products ofcombustion, said products also termed combustion gases, generallyoccupying regions 28, 35, the gas side of 36, and 42, exiting as 43.

FIG. 19, given its general system description provided above, isapplicable to a wide variety of fossil-fired systems including acoal-burning power plant, an oil-burning power plant, a gas-fired powerplant, a biomass combustor, a fluidized bed combustor, a conventionalelectric power plant, a steam generator, a package boiler, a combustionturbine, a combustion turbine with a heat recovery boiler, a peatburning power plant, and a Recovery Boiler used in the pulp and paperindustry. This list is not meant to be exhaustive, however, and ispresented to illustrate some of the areas of applicability of thepresent invention which encompass any thermal system burning a fossilfuel and which has at least one heat exchanger whose working fluid isbeing heated by the products of combustion. This invention is applicableto a wide variety of Input/Loss methods.

Within fossil-fired systems, some quantities are readily measured withadequate accuracy, and others may not be measured on-line (in real time)with accuracy sufficient to quantify the operation of the system 20 tothe required accuracy to optimize efficiency. For example, working fluidflows, pressures and temperatures may be readily measured with goodaccuracy by conventional sensors located at defined boundaries such as134, 130, 25, 33, 42, 29 and 31. Choice Operating Parameters all may,under ideal conditions, be directly measured with common industrialaccuracy either in real time or periodically, then corrected using themethods of '877 if required. In FIG. 19 quantities which may be (or are)Choice Operating Parameters include: the combustion gas concentrationsin the regions 35 and 42 (including CO₂, H₂O, and O₂, termed Λ_(1B),Λ_(2B), Λ_(7B) at region 35, and Λ_(1S), Λ_(2S), Λ_(7S) at region 42);the indicated combustion air flow 24 (when combined with indicated plantfuel flow 22 then allows the Air/Fuel ratio to be determined, Λ₃, whichallows the fuel ash fraction to be computed); the ratio of gasconcentrations across the air pre-heater, regions 35 and 42 (either theO₂ or the CO₂ ratio across these regions, preferably the CO₂ ratio, thusallowing the Air Pre-Heater Leakage Factor R_(Act) to be determined,Λ₄); the concentration of O₂ in the combustion air local to the system25 (termed A_(Act), or Λ₅, allowing φ_(Act) to be determined); theindicated plant limestone flow 31 (Λ₆); and the relative humidityassociated with the combustion air local to the system 25 (Λ_(g)). Inaddition, another Choice Operating Parameter is tube leakage flow, notshown (Λ₈), which may be determined by optimizing the fuel's averagewater content in the fuel or using the computed As-Fired fuel flow(m_(AF)); when optimized, the tube leakage flow becomes defined,consistent with stoichiometrics of Eqs. (29F) through the term b_(Z).Refer to Eqs. (111S) through (119). This invention teaches to employ'877 methods to correct such measurements or their assumptions if suchmeasurements are not available.

FIG. 20 illustrates an important portion of this invention, specificallythe general calculational sequences associated with The Input/LossMethod. Boxs 110, 120 and 130 represents general data initializationsteps including using or developing a genetics of the fossil fuel, datacollection, data organization and routine set-ups of all programs. Box250 initiates continuous on-line monitoring of a thermal system. Box 255depicts obtaining a set of correction factors for Choice OperatingParameters by either applying judgement based on a power engineer'sexperience with a particular instrument resulting in a set of obtainedcorrection factors, or through use of the ERR-CALC program resulting ina set of correction factors based on a multidimensional minimizationanalysis (whose methods are taught herein, and further discussed in'877). If correction factors are not to be updated at the same frequencyas the Fuel Iterations (defined below), Box 255 is bypassed; and, ifbypassed, its previously computed correction factors are applied to Apt,then employed within the Fuel Iterations. Box 260 depicts the FUELprogram which reduces fuel data from identified multiple sources,including an estimate of the unknown fuel, prepares a composite fuel,and then prepares an input file for the system simulator EX-FOSS.Reduction of fuel data involves combining the primary (computed) fuelchemistry from a previous iteration, with secondary fuels which haveconstant and known chemistries, producing a composite fuel. Box 270 issystem data acquired from the process as on-line (in essentially realtime) including at least the following Operating Parameters (refer tothe section entitled MEANING OF TERMS for details): working fluidpressures, temperatures and flows, air psychrometrics, useful systemoutput, Air pre-Heater Leakage Factor, and other related data. Box 280depicts the system simulator EX-FOSS which, given an input of acomposite fuel chemistry and composite calorific value from FUEL, inputsfrom Box 270, and routine set-up data, produces the following: boilerefficiency using the methods of '429, As-Fired fuel flow (m_(AF)) usingEq. (103), complete effluent concentrations of Eq. (29F), systemefficiency and heat rate terms using Eqs. (104A) through (107B),effluent mass flow using the summation of Eq. (108), effluent volumetricflow using Eq. (110), emission rates of all effluents including thecommon pollutants using Eq. (109B), and other thermal performanceparameters including, for example, energy flow to the working fluidheated by combustion products (BBTC), and the Firing Correction (HBC)which may be taken as zero. The determination of many of theseparameters is taught herein, others are taught in '994 and '429. Box 285depicts the HEATRATE program within which, given the corrected ChoiceOperating Parameters, produces fuel chemistry, the L₁₀ Factor of Eq.(70), and fuel calorific value for both the composite fuel (as eithergross or net values), and, given the known compositions of secondaryfuels, the composition of the primary (unknown) fuel is then computed.Designation 287 tests for convergence of the process based on compositefuel moles (x), certain effluents such as CO₂ and H₂O, calorific valueand computed fuel water fraction; if the convergence criteria is not metthe process continues to iterate from Box 260. In general, convergenceslie within 0.5×10⁻⁴ percent of the computed As-Fired fuel moles. Notethat the iterations encompassing 260, 270, 280, 285 and 287 define whatis meant by “Fuel Iterations”. In summary, Fuel Iterations are theiterative calculations between EX-FOSS, as input with a known fuelchemistry and calorific value from a previous iteration, but withunknown effluents (to be computed by EX-FOSS, except for effluent O₂which is input); and HEATRATE as input with known effluents (i.e., thecorrected Choice Operating Parameters), but with unknown fuel chemistryand calorific value (to be computed by HEATRATE). If the convergencecriteria is met, Box 292 then reports the final effluent and emissioninformation. Typically, monitoring cycles are scheduled for every 2, 3or 4 minutes using updated data based on 15 minute running averages.Once converged and all computations have been completed, Box 294produces reportable results from the EX-FOSS and HEATRATE. Resultsinclude thermal performance information whereby improvements may be had,and provides reports to regulatory authorities. Box 296 represents adecision to return to Box 255 for another monitoring cycle (which may beautomated). Box 298 of FIG. 20 is to quit.

FIG. 22 is a representation of the apparatus of this invention showing acomputer receiving acquired system data, such as Operating Parameters,from a data acquisition device and producing output reports via aprogrammed computed. Specifically the represented power plant of FIG.22, with item numbers corresponding to FIG. 19, and meaning the same asdescribed for FIG. 19, is instrumented such that Operating Parameterdata and selected Choice Operating Parameter (COP) data are collected ina data acquisition device 400. Within the data acquisition device 400said data is typically converted to engineering units, averaged and/orarchived, resulting in a set of acquired system data. Examples of saiddata acquisition device 400 include a data acquisition system, aDistributed Control System, an analog signal to digital signalconversion device, a pneumatic signal to digital signal conversiondevice, an auxiliary computer collecting data, or an electronic devicewith data collection and/or conversion features. After processing, thedata acquisition device 400 transfers the set of acquired system data410 to a computer 420 with a processing means and a memory means. Theprocessing vehicle for transfer of the set of acquired system data 410may be either by wire or by wireless transmission. The computer 420 isprogrammed with procedures which determine a complete As-Fired fuelchemistry, including fuel water and fuel ash. The computer 420 is alsoprogrammed with procedures which determine an Ultimate Analysis as asub-set of a complete As-Fired fuel chemistry. The computer 420,operating with the programmed procedures descriptive of this disclosureproduces at least a complete As-Fired fuel chemistry based on thegenetics of a fossil fuel and a mathematical description of the thermalsystem. If 420 is programmed with the procedures descriptive of any oneof the Input/Loss methods, the computer 420 produces at least anUltimate Analysis based on stoichiometric descriptions of the combustionprocess. The computer 420, operating with the programmed proceduresdescriptive of this disclosure, also may determine any one or all of thefollowing as taught herein: the fuel's calorific value, the energy flowto the working fluid heated by combustion products (BBTC) 33, boilerefficiency, fuel mass flow 22, effluent mass flow 43, effluentvolumetric flow 43, emission rates of the pollutants, and/or systemthermal efficiency. Instrumentation indicted in FIG. 22 includes Stacktemperature 302 (also termed the effluent temperature), Stack O₂ (theCOP Λ_(1S)) 304, Stack CO₂ (the COP Λ_(1S)) 306, and Stack H₂O (the COPΛ_(2S)) 308. The COP for the concentration of O₂ in the combustion air(Λ₅) 310, using the symbol A_(Act) in FIG. 22 and as taught above, isobtained either from instrumentation, from the United States NationalAeronautics and Space Administration, or otherwise obtained byassumption or estimation, the value of which may then be corrected astaught in '877. The COP for the Air Pre-Heater Leakage Factor (A₄) 312,using the symbol R_(Act) in FIG. 22 and as taught above, is obtainedeither from instrumentation as the ratio of CO₂ across the AirPre-Heater 36 requiring CO₂ instruments at 35 and 42, or otherwiseobtained by assumption or estimation based on the system operator'sjudgement, the value of which may then be corrected as taught in '877.These COPs represent an example of a selection of COPs, considered themost important; for other COPs see Eqs. (111S) through (119). The energyflow to the working fluid heated by combustion products (BBTC) derivesfrom turbine cycle instrumentation. Said turbine cycle instrumentation,in a general fashion, is suggested by the following: steam pressure 314,steam temperature 316, feedwater pressure 318, feedwater temperature 320and feedwater flow 322. All of these signals are transmitted to the dataacquisition device 400 for processing. The determination of the steamenthalpy from pressure 314 and temperature 316 data, and determinationof feedwater enthalpy from pressure 318 and temperature 320 data mayoccur within 400 or may occur within the computer 420. Furtherdiscussion of BBTC is provide under the MEANING OF TERMS, including thepresence of a Reheater (not shown in FIG. 22). Output 430 consists ofany one or all of the following quantities: complete As-Fired fuelchemistry, fuel calorific value, the energy flow to the working fluidheated by combustion products (BBTC), boiler efficiency, fuel mass flow,effluent mass flow, effluent volumetric flow, emission rates of thepollutants and/or system thermal efficiency. Output 430 may be madeavailable to the system operator as paper reports printed on a printer440, or may be made available to the system operator in electronic orvisual forms using the computer 420. In summary, this invention teachesto operate a computer 420 to obtain a complete As-Fired fuel chemistry,including fuel water and fuel ash, based on the genetics of the fossilfuel, the mathematical description, the set of measurable OperatingParameters, the obtained effluent H₂O, the obtained fuel ashconcentration, the concentration of O₂ in the combustion air local tothe system and the Air Pre-Heater Leakage Factor.

1-45. (canceled)
 46. A method for quantifying the operation of a thermalsystem burning a fossil fuel having a heat exchanger/combustion regionproducing combustion products, the method comprising the steps of:operating a computer programmed with a mathematical description of thethermal system based on a closed-form solution, resulting in aprogrammed computer; obtaining a set of Choice Operating Parametersselected from the group consisting of: a Stack CO₂, a Boiler CO₂, aStack H₂O, a Boiler H₂O, an Air Pre-Heater Leakage Factor, aconcentration of O₂ in the combustion air local to the thermal system,an indicated plant limestone flow, a Stack O₂, a Boiler O₂, and arelative humidity of the ambient air local to the thermal system;obtaining a fuel ash concentration selected from the group consistingof: a constant value of fuel ash, a predictable value of fuel ash, ameasured value of fuel ash determined from a fuel ash instrument and avalue of fuel ash determined from an explicit solution, as an obtainedfuel ash concentration; and operating the programmed computer to obtaina complete As-Fired fuel chemistry, including fuel water and fuel ash,based on the mathematical description of the thermal system, the set ofChoice Operating Parameters, and the obtained fuel ash concentration.47. A method for quantifying the operation of a thermal system burning afossil fuel having a heat exchanger/combustion region producingcombustion products, the method comprising the steps of: before on-lineoperation, developing a mathematical description of the thermal systembased on a closed-form solution; while operating on-line, the step ofoperating on-line comprising the steps of obtaining a set of ChoiceOperating Parameters selected from the group consisting of: a Stack CO₂,a Boiler CO₂, a Stack H₂O, a Boiler H₂O, an Air Pre-Heater LeakageFactor, a concentration of O₂ in the combustion air local to the thermalsystem, an indicated plant limestone flow, a Stack O₂, a Boiler O₂, anda relative humidity of the ambient air local to the thermal system,obtaining a fuel ash concentration selected from the group consistingof: a constant value of fuel ash, a predictable value of fuel ash, ameasured value of fuel ash determined from a fuel ash instrument and avalue of fuel ash determined from an explicit solution, as an obtainedfuel ash concentration, and operating a programmed computer to obtain acomplete As-Fired fuel chemistry, including fuel water and fuel ash,based on the mathematical description of the thermal system, the set ofChoice Operating Parameters, and the obtained fuel ash concentration.48. A method for quantifying the operation of a thermal system burning afossil fuel having a heat exchanger/combustion region producingcombustion products, the method comprising the steps of: operating acomputer programmed with a mathematical description of the thermalsystem based on stoichiometric relationships and genetics of the fossilfuel, resulting in a programmed computer, obtaining a set of ChoiceOperating Parameters selected from the group consisting of: a Stack CO₂,a Boiler CO₂, a Stack H₂O, a Boiler H₂O, an Air Pre-Heater LeakageFactor, a concentration of O₂ in the combustion air local to the thermalsystem, an indicated plant limestone flow, a Stack O₂, a Boiler O₂, anda relative humidity of the ambient air local to the thermal system;obtaining a fuel ash concentration selected from the group consistingof: a constant value of fuel ash, a predictable value of fuel ash, ameasured value of fuel ash determined from a fuel ash instrument and avalue of fuel ash determined from an explicit solution, as an obtainedfuel ash concentration; and operating the programmed computer to obtaina complete As-Fired fuel chemistry, including fuel water and fuel ash,based on the mathematical description of the thermal system, the set ofChoice Operating Parameters, and the obtained fuel ash concentration.49. A method for quantifying the operation of a thermal system burning afossil fuel having a heat exchanger/combustion region producingcombustion products, the method comprising the steps of: before on-lineoperation, developing a mathematical description of the thermal systembased on combustion stoichiometrics and a genetics of the fossil fuel;while operating on-line, the step of operating on-line comprising thesteps of obtaining a set of Choice Operating Parameters selected fromthe group consisting of: a Stack CO₂, a Boiler CO₂, a Stack H₂O, aBoiler H₂O, an Air Pre-Heater Leakage Factor, a concentration of O₂ inthe combustion air local to the thermal system, an indicated plantlimestone flow, a Stack O₂, a Boiler O₂, and a relative humidity of theambient air local to the thermal system; obtaining a fuel ashconcentration selected from the group consisting of: a constant value offuel ash, a predictable value of fuel ash, a measured value of fuel ashdetermined from a fuel ash instrument and a value of fuel ash determinedfrom an explicit solution, as an obtained fuel ash concentration; andoperating a programmed computer to obtain a complete As-Fired fuelchemistry, including fuel water and fuel ash, based on the mathematicaldescription of the thermal system, the set of Choice OperatingParameters, and the obtained fuel ash concentration.
 50. A method forquantifying the operation of a thermal system burning a fossil fuelhaving a heat exchanger/combustion region producing combustion products,the method comprising the steps of: operating a computer programmed witha mathematical description of the thermal system based on stoichiometricrelationships and genetics of the fossil fuel, resulting in a programmedcomputer, measuring a set of measurable Operating Parameters, includingat least effluent concentrations of O₂ and CO₂, these measurements beingmade at a location downstream of the heat exchanger/combustion region ofthe thermal system, obtaining an effluent concentration of H₂O, as anobtained effluent H₂O, obtaining a fuel ash concentration selected fromthe group consisting of: a constant value of fuel ash, a predictablevalue of fuel ash, a measured value of fuel ash determined from a fuelash instrument and a value of fuel ash determined from an explicitsolution, as an obtained fuel ash concentration, obtaining aconcentration of O₂ in the combustion air local to the system, obtainingan Air Pre-Heater Leakage Factor, and operating the programmed computerto obtain a complete As-Fired fuel chemistry, including fuel water andfuel ash, based on the mathematical description of the thermal system,the set of measurable Operating Parameters, the obtained effluent H₂O,the obtained fuel ash concentration, the concentration of O₂ in thecombustion air local to the system and the Air Pre-Heater LeakageFactor.
 51. A method for quantifying the operation of a thermal systemburning a fossil fuel having a heat exchanger/combustion regionproducing combustion products, the method comprising the steps of:before on-line operation, developing a mathematical description of thethermal system based on stoichiometric relationships and genetics of thefossil fuel; the step of operating on-line comprising the steps ofmeasuring a set of measurable Operating Parameters, including at leasteffluent concentrations of O₂ and CO₂, these measurements being made ata location downstream of the heat exchanger/combustion region of thethermal system, obtaining an effluent concentration of H₂O, as anobtained effluent H₂O, obtaining a fuel ash concentration selected fromthe group consisting of: a constant value of fuel ash, a predictablevalue of fuel ash, a measured value of fuel ash determined from a fuelash instrument and a value of fuel ash determined from an explicitsolution, as an obtained fuel ash concentration, obtaining aconcentration of O₂ in the combustion air local to the system, obtainingan Air Pre-Heater Leakage Factor, and operating a programmed computer toobtain a complete As-Fired fuel chemistry, including fuel water and fuelash, based on the mathematical description of the thermal system, theset of measurable Operating Parameters, the obtained effluent H₂O, theobtained fuel ash concentration, the concentration of O₂ in thecombustion air local to the system and the Air Pre-Heater LeakageFactor.
 52. The method of claims 46, 47, 48, 49, 50 or 51, wherein thethermal system comprises a thermal system selected from the groupconsisting of: a coal-burning power plant, a lignite-burning powerplant, an oil-burning power plant, a gas-fired power plant, a biomasscombustor, a fluidized bed combustor, a conventional electric powerplant, a steam generator, a package boiler, a combustion turbine, acombustion turbine with a heat recovery boiler, a power plant burningIrish peat, and a Recovery Boiler used in the pulp and paper industry.53. The method of claims 46, 47, 48, 49, 50 or 51, wherein the step ofoperating the programmed computer to obtain the complete As-Fired fuelchemistry includes the steps of operating the programmed computer toobtain a fuel chemistry including at least one fuel constituent selectedfrom the group consisting of: weight percent carbon, weight percenthydrogen and weight percent oxygen of the fuel, and calculating a fuelcalorific value based on the fuel chemistry in units of kJ/kg, the stepof calculating including a step of forming products of numericalcoefficients times the weight percent of the fuel constituent, whereinat least one of the numerical coefficients is selected from the groupconsisting of from 325 to 358 for weight percent carbon, from 896 to1454 for weight percent hydrogen, and from −86 to −181 for weightpercent oxygen and combinations thereof.
 54. The method of claims 46,47, 48, 49, 50 or 51, wherein the step of operating the programmedcomputer to obtain the complete As-Fired fuel chemistry includes thesteps of operating the programmed computer to obtain a fuel chemistryincluding at least one fuel constituent selected from the groupconsisting of: weight percent carbon, weight percent hydrogen and weightpercent oxygen of the fuel, and calculating a fuel calorific value basedon the fuel chemistry in units of Btu per pound-mass, the step ofcalculating including a step of forming products of numericalcoefficients times the weight percent of the fuel constituent, whereinat least one of the numerical coefficients is selected from the groupconsisting of from 140 to 154 for weight percent carbon, from 385 to 625for weight percent hydrogen, and from −37 to −78 for weight percentoxygen and combinations thereof.
 55. The method of claims 46, 47, 48,49, 50 or 51, wherein the step of obtaining the concentration of O₂ inthe combustion air local to the system includes the step of using aconcentration of O₂ in the combustion air local to the system obtainedfrom the United States National Aeronautics and Space Administration.56. The method of claims 46, 48 or 50, wherein the step of operating thecomputer programmed with the mathematical description of the thermalsystem, includes the step of operating the computer programmed with themathematical description of the thermal system based on one of theInput/Loss methods.
 57. The method of claims 47, 49 or 51, wherein thestep of developing the mathematical description of the thermal system,includes the step of developing the mathematical description of thethermal system based on one of the Input/Loss methods.
 58. The method ofclaims 46, 48 or 50, wherein the step of operating the computerprogrammed with the mathematical description of the thermal system,includes the step of operating the computer programmed with themathematical description of the thermal system based on matrix solution.59. The method of claims 47, 49 or 51, wherein the step of developingthe mathematical description of the thermal system, includes the step ofdeveloping the mathematical description of the thermal system based onmatrix solution.
 60. The method of claims 46, 47, 48 or 49, including,after the step of operating the programmed computer to obtain thecomplete As-Fired fuel chemistry, the additional steps of obtaining acorrected L₁₀ Factor based on the complete As-Fired fuel chemistry;establishing a reference L₁₀ Factor; operating the programmed computerto obtain a multidimensional minimization analysis based on minimizingerror between the corrected L₁₀ Factor and the reference L₁₀ Factor,such that at least one Choice Operating Parameter of a set of ChoiceOperating Parameters is corrected, the set of Choice OperatingParameters selected from the group consisting of: effluent concentrationof CO₂, effluent concentration of O₂, the obtained effluent H₂O, theconcentration of O₂ in the ambient air entering the thermal system andthe Air Pre-Heater Leakage Factor resulting in a set of correctionfactors; and operating the programmed computer by applying in subsequenton-line analysis the set of correction factors to the set of ChoiceOperating Parameters.
 61. The method of claims 46, 47, 48 or 49, afterthe step of operating the programmed computer to obtain the completeAs-Fired fuel chemistry, the additional step which comprises operatingthe programmed computer to obtain an As-Fired fuel calorific value as afunction of the complete As-Fired fuel chemistry.
 62. The method ofclaim 61, after the step of operating the programmed computer to obtainan As-Fired fuel calorific value, the additional steps which comprisemeasuring an effluent temperature of the combustion gas, operating theprogrammed computer to obtain a boiler efficiency as a function of thecomplete As-Fired fuel chemistry, the set of Choice OperatingParameters, the As-Fired fuel calorific value and the effluenttemperature.
 63. The method of claim 61, after the step of operating theprogrammed computer to obtain the As-Fired fuel calorific value, theadditional steps which comprise obtaining a set of effluentconcentrations including at least effluent SO₂, and operating theprogrammed computer to obtain individual emission rates based on theAs-Fired fuel calorific value and the set of effluent concentrations.64. The method of claim 62, after the step of operating the programmedcomputer to obtain the boiler efficiency, the additional steps whichcomprise measuring an electrical generation produced from the thermalsystem, measuring an energy flow to the working fluid heated bycombustion products; and operating the programmed computer to obtain asystem thermal efficiency as a function of the boiler efficiency, theelectrical generation produced, and the energy flow to the workingfluid.
 65. The method of claim 62, after the step of operating theprogrammed computer to obtain the boiler efficiency, the additionalsteps which comprise measuring an energy flow to the working fluidheated by combustion products, and operating the programmed computer toobtain an As-Fired fuel flow based on the boiler efficiency, theAs-Fired fuel calorific value, and the energy flow to the working fluid.66. The method of claim 65, after the step of operating the programmedcomputer to obtain the As-Fired fuel flow, the additional step whichcomprises operating the programmed computer to obtain a total effluentflow based on the As-Fired fuel flow.
 67. The method of claim 65, afterthe step of operating the programmed computer to obtain the As-Firedfuel flow, the additional steps which comprise obtaining a set ofeffluent concentrations including at least effluent SO₂, and operatingthe programmed computer to obtain individual effluent flows based on theset of effluent concentrations and the As-Fired fuel flow.
 68. Themethod of claim 65, including, after the step of operating theprogrammed computer to obtain the As-Fired fuel flow, the additionalsteps which comprise obtaining an indicated plant fuel flow associatedwith the thermal system; operating the programmed computer to perform amultidimensional minimization analysis based on minimizing error betweenthe As-Fired fuel flow and the indicated plant fuel flow, such that atleast one Choice Operating Parameter of a set of Choice OperatingParameters is corrected, the set of Choice Operating Parameters selectedfrom the group consisting of: effluent concentration of CO₂, effluentconcentration of O₂, the obtained effluent H₂O, the concentration of O₂in the ambient air entering the thermal system and the Air Pre-HeaterLeakage Factor resulting in a set of correction factors; and operatingthe programmed computer by applying in subsequent analysis the set ofcorrection factors to the set of Choice Operating Parameters.
 69. Themethod of claim 65, after the step of operating the programmed computerto obtain the As-Fired fuel flow, the additional steps which compriseobtaining a gas density and a molecular weight of the effluent gas, andoperating the programmed computer to obtain an effluent volumetric flowbased on the As-Fired fuel flow, the gas density and the molecularweight of the effluent gas.
 70. The method of claims 50 or 51, after thestep of operating the programmed computer to obtain the completeAs-Fired fuel chemistry, the additional step comprising of operating theprogrammed computer to obtain an As-Fired fuel calorific value as afunction of the complete As-Fired fuel chemistry.
 71. The method ofclaim 70, wherein the step of measuring the set of measurable OperatingParameters includes the step of measuring an effluent temperature; andwherein the method further includes an additional step, after the stepof operating the programmed computer to obtain a complete As-Fired fuelchemistry, of operating the programmed computer to obtain a boilerefficiency as a function of the complete As-Fired fuel chemistry, theeffluent temperature, effluent concentrations and the As-Fired fuelcalorific value.
 72. The method of claim 70, after the step of operatingthe programmed computer to obtain the As-Fired fuel calorific value, theadditional steps comprising obtaining a set of effluent concentrationsincluding at least effluent SO₂, and operating the programmed computerto obtain individual emission rates based on the As-Fired fuel calorificvalue and the set of effluent concentrations.
 73. The method of claim71, wherein the step of measuring the set of measurable OperatingParameters includes the steps of measuring an electrical generationproduced from the thermal system, and measuring an energy flow to theworking fluid heated by combustion products; and wherein the methodfurther includes an additional step, after the step of operating theprogrammed computer to obtain a boiler efficiency, of operating theprogrammed computer to obtain a system thermal efficiency as a functionof the electrical generation produced, the energy flow to the workingfluid and the boiler efficiency.
 74. The method of claim 71, wherein thestep of measuring the set of measurable Operating Parameters includesthe step of measuring an energy flow to the working fluid heated bycombustion products; and wherein the method further includes anadditional step, after the step of operating the programmed computer toobtain a boiler efficiency, of operating the programmed computer toobtain an As-Fired fuel flow based on the boiler efficiency, theAs-Fired fuel calorific value, and the energy flow to the working fluid.75. The method of claim 74, after the step of operating the programmedcomputer to obtain the As-Fired fuel flow, an additional step comprisingoperating the programmed computer to obtain a total effluent flow basedon the As-Fired fuel flow.
 76. The method of claim 74, after the step ofoperating the programmed computer to obtain the As-Fired fuel flow, theadditional steps comprising obtaining a set of effluent concentrationsincluding at least effluent SO₂, and operating the programmed computerto obtain individual effluent flows based on the set of effluentconcentrations and the As-Fired fuel flow.
 77. The method of claim 74,including, after the step of operating the programmed computer to obtainthe As-Fired fuel flow, the additional steps of obtaining an indicatedplant fuel flow associated with the thermal system; operating theprogrammed computer to obtain a multidimensional minimization analysisbased on minimizing error between the As-Fired fuel flow and theindicated plant fuel flow, such that at least one Choice OperatingParameter of a set of Choice Operating Parameters is corrected, the setof Choice Operating Parameters selected from the group consisting of:effluent concentration of CO₂, effluent concentration of O₂, theobtained effluent H₂O, the concentration of O₂ in the ambient airentering the thermal system and the Air Pre-Heater Leakage Factorresulting in a set of correction factors; and operating the programmedcomputer by applying in subsequent analysis the set of correctionfactors to the set of Choice Operating Parameters.
 78. The method ofclaim 74, after the step of operating the programmed computer to obtainthe As-Fired fuel flow, the additional steps comprising obtaining astandard density of the effluent gas, obtaining an average molecularweight of the effluent gas, and operating the programmed computer toobtain a total effluent dry volumetric flow based on the As-Fired fuelflow, the standard density and the average molecular weight of theeffluent gas.
 79. The method of claims 50 or 51, wherein the step ofmeasuring the set of measurable Operating Parameters includes anadditional step of obtaining a set of effluent concentrations, the setof effluent concentrations containing at least one selected from thegroup consisting of: CO, SO₂ and NO_(X), resulting in a set of pollutantconcentrations; and wherein the step of operating the programmedcomputer to obtain a complete As-Fired fuel chemistry includes the stepof operating the programmed computer to obtain the complete As-Firedfuel chemistry, including fuel water and fuel ash, based on themathematical description of the thermal system, the set of measurableOperating Parameters, the obtained effluent H₂O, the obtained fuel ashconcentration, the concentration of O₂ in the combustion air local tothe system, the Air Pre-Heater Leakage Factor, and the set of effluentpollutant concentrations.
 80. The method of claims 46, 48 or 50, whereinthe step of operating the computer programmed with the mathematicaldescription of the thermal system includes the additional step, ofoperating the computer programmed with the mathematical description ofthe thermal system based on stoichiometric relationships and genetics ofthe fossil fuel in the form CH_(c2)O_(c3), the reduced value c3 selectedfrom the group consisting of a value from 0.009 to 0.024 for anthracitecoal, from 0.025 to 0.054 for semi-anthracite coal, from 0.055 to 0.121for the coal Ranks of hvAb and hvBb, from 0.122 to 0.170 forsub-bituminous A coal, from 0.171 to 0.183 for Powder River Basin coal,from 0.184 to 0.200 for sub-bituminous B coal, from 0.201 to 0.215 forsub-bituminous C coal, from 0.216 to 0.230 for lignite A, from 0.390 to0.458 for Greek lignite, and from 0.459 to 0.520 for Irish peat, andcombinations thereof.
 81. The method of claims 47, 49 or 51, wherein thestep of developing the mathematical description of the thermal systemincludes the additional step, of developing the mathematical descriptionof the thermal system based on stoichiometric relationships and geneticsof the fossil fuel in the form CH_(c2)O_(c3), the reduced value c3selected from the group consisting of a value from 0.009 to 0.024 foranthracite coal, from 0.025 to 0.054 for semi-anthracite coal, from0.055 to 0.121 for the coal Ranks of hvAb and hvBb, from 0.122 to 0.170for sub-bituminous A coal, from 0.171 to 0.183 for Powder River Basincoal, from 0.184 to 0.200 for sub-bituminous B coal, from 0.201 to 0.215for sub-bituminous C coal, from 0.216 to 0.230 for lignite A, from 0.390to 0.458 for Greek lignite, and from 0.459 to 0.520 for Irish peat, andcombinations thereof.
 82. The method of claims 46, 47, 48 or 49, whereinthe step of obtaining the set of Choice Operating Parameters includesobtaining a set of Choice Operating Parameters selected from the groupconsisting of: a Stack CO₂, a Boiler CO₂, a Stack H₂O, a Boiler H₂O, anAir Pre-Heater Leakage Factor, a concentration of O₂ in the combustionair local to the thermal system, an indicated plant limestone flow, aStack O₂, a Boiler O₂, a relative humidity of the ambient air local tothe thermal system, and a tube leakage flow rate.
 83. The method ofclaims 46, 47, 48 or 49, after the step of operating the programmedcomputer to obtain the complete As-Fired fuel chemistry, the additionalstep comprising operating the programmed computer to obtain a set ofcorrection factors to be applied to the set of Choice OperatingParameters, the set of Choice Operating Parameters selected from thegroup consisting of: effluent concentration of O₂, effluentconcentrations of CO₂, the concentration of O₂ in the combustion airlocal to the system and the Air Pre-Heater Leakage Factor, the set ofcorrection factors selected from the group consisting of: a set ofobtained correction factors, and a set of correction factors based on amultidimensional minimization analysis.
 84. The method of claims 46, 47,48 or 49, wherein the step of operating the programmed computer toobtain the complete As-Fired fuel chemistry, comprises the step ofoperating the programmed computer to obtain an Ultimate Analysis of thefuel chemistry based on the mathematical description of the thermalsystem, the set of Choice Operating Parameters and the obtained fuel ashconcentration.
 85. The method of claims 50 or 51, wherein the step ofoperating the programmed computer to obtain the complete As-Fired fuelchemistry, comprises the step of operating the programmed computer toobtain an Ultimate Analysis of the fuel chemistry based on themathematical description of the thermal system, said mathematicaldescription based on stoichiometric relationships and genetics of thefossil fuel, the set of measurable Operating Parameters, the obtainedeffluent H₂O, the concentration of O₂ in the combustion air local to thesystem and the Air Pre-Heater Leakage Factor.